{"id":32297,"date":"2022-02-06T21:19:42","date_gmt":"2022-02-06T13:19:42","guid":{"rendered":"https:\/\/swarma.org\/?p=32297"},"modified":"2022-02-06T21:19:42","modified_gmt":"2022-02-06T13:19:42","slug":"%e5%a4%8d%e6%9d%82%e7%b3%bb%e7%bb%9f%e4%b8%ad%e7%9a%84%e7%aa%81%e5%8f%98%e7%89%b9%e5%88%8a-%e7%90%86%e8%ae%ba%e3%80%81%e6%96%b9%e6%b3%95%e4%b8%8e%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32297","title":{"rendered":"\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u7a81\u53d8\u7279\u520a\u2014\u2014\u7406\u8bba\u3001\u65b9\u6cd5\u4e0e\u5e94\u7528"},"content":{"rendered":"
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<\/strong>\u4e34\u754c\u4e0e\u7a81\u53d8\u73b0\u8c61\uff08critical and tipping\uff09\u662f\u590d\u6742\u7cfb\u7edf\u79d1\u5b66\u7684\u91cd\u8981\u7814\u7a76\u5bf9\u8c61\u3002\u8fd1\u671fThe European Physical Journal <\/em>\u53d1\u5e03\u4e13\u9898\u7279\u520a\uff0c\u901a\u8fc7 21 \u7bc7\u6587\u7ae0\u63a2\u8ba8\u4e86\u590d\u6742\u7cfb\u7edf\u4e2d\u4e34\u754c\u70b9\u7684\u6027\u8d28\u3002\u8fd9\u4e9b\u7814\u7a76\u63ed\u793a\u4e86\u8be5\u9886\u57df\u7684\u6700\u65b0\u8d8b\u52bf\u548c\u7814\u7a76\u65b9\u5411\uff0c\u5e76\u5f3a\u8c03\u4e86\u8be5\u9886\u57df\u5728\u672a\u6765\u5c06\u9762\u4e34\u7684\u7d27\u8feb\u6311\u6218\u3002\u8be5\u7279\u520a\u4e2d\u7684\u6587\u7ae0\u5206\u4e3a\u4e09\u5927\u90e8\u5206\uff1a\u7b2c\u4e00\u90e8\u5206\u96c6\u4e2d\u8ba8\u8bba\u4e86\u80fd\u591f\u8bf1\u53d1\u4e0d\u540c\u72b6\u6001\u4e4b\u95f4\u7a81\u53d8\u7684\u673a\u5236\uff1b\u7b2c\u4e8c\u90e8\u5206\u63a2\u8ba8\u4e86\u8868\u5f81\u7a81\u53d8\u73b0\u8c61\u7684\u63aa\u65bd\uff0c\u5e76\u63d0\u51fa\u4e86\u53ef\u7528\u4e8e\u63a7\u5236\u7a81\u53d8\u7684\u7b56\u7565\uff1b\u7b2c\u4e09\u90e8\u5206\u4ecb\u7ecd\u4e86\u590d\u6742\u7cfb\u7edf\u4e2d\u7a81\u53d8\u7684\u51e0\u4e2a\u5177\u4f53\u6848\u4f8b\u7814\u7a76\uff0c\u5982\u4ea4\u901a\u6d41\u3001\u964d\u6c34\u6a21\u5f0f\u548c\u5c18\u4e91\u4e0d\u7a33\u5b9a\u6027\u3002\u672c\u6587\u7f16\u8bd1\u4e86\u7279\u520a\u5bfc\u8a00\u548c21\u7bc7\u8bba\u6587\u6458\u8981\u3002<\/span><\/strong><\/span><\/p>\n


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\u7814\u7a76\u9886\u57df\uff1a\u4e34\u754c\u73b0\u8c61\uff0c\u7a81\u53d8\uff0c\u590d\u6742\u7cfb\u7edf\uff0c\u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff0c\u6570\u636e\u9a71\u52a8<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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G. Ambika, J\u00fcrgen Kurths<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/p>\n

\u738b\u767e\u81fb<\/span> <\/span>| \u8bd1\u8005<\/strong><\/span><\/span><\/strong><\/span><\/p>\n

\u5218\u57f9\u6e90<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span>
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\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span>
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\u7279\u520a\u540d\u79f0\uff1a<\/span>
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Tipping in Complex Systems: Theory, Methods and Applications<\/span><\/p>\n

\u7279\u520a\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/journal\/11734\/topicalCollection\/AC_ac67ae404e16f19b99913247f14b8072<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5bfc\u8a00\uff1a\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u7a81\u53d8\uff1a\u7406\u8bba\u3001\u65b9\u6cd5\u4e0e\u5e94\u7528<\/strong><\/span><\/h3>\n

1. \u5bf9\u79f0\u7834\u574f\u5f15\u8d77\u7684\u7a81\u53d8\u8001\u5316<\/span><\/strong><\/span><\/p>\n

2. \u9884\u671f\u8bf1\u53d1\u7684\u793e\u4f1a\u503e\u5411\u6027\uff1a\u793e\u4f1a\u52a8\u529b\u5b66\u80fd\u7a33\u5b9a\u73af\u5883\u5417?<\/strong><\/span><\/h3>\n

3. \u590d\u6742\u7f51\u7edc\u4ea4\u901a\u6d41Nagel-Schreckenberg\u6a21\u578b\u4e2d\u7684\u6781\u7aef\u4e8b\u4ef6<\/strong><\/span><\/h3>\n
4. <\/span><\/strong>\u975e\u7ebf\u6027\u632f\u8361\u5668\u4e2d\u52a8\u6001\u7fa4\u4f53\u611f\u5e94\u5f71\u54cd\u7684\u4e34\u754c\u8f6c\u53d8<\/span><\/strong><\/span><\/section>\n
5. <\/span><\/strong>\u7a7a\u95f4\u751f\u6001\u7cfb\u7edf\u4e2d\u901f\u7387\u8bf1\u5bfc\u7684\u7a81\u53d8\u4e0e\u5236\u5ea6\u53d8\u8fc1<\/span><\/strong><\/span><\/section>\n
6. <\/span><\/strong>\u751f\u6001\u7cfb\u7edf\u4e2d\u7531\u901f\u7387\u5bfc\u81f4\u7684\u7a33\u6001\u8f6c\u53d8<\/span><\/strong><\/span><\/section>\n

7. <\/span><\/strong>\u6e10\u8fd1\u81ea\u6cbb\u7cfb\u7edf\u6df7\u6c8c\u5438\u5f15\u5b50\u7684\u7269\u7406\u4e0d\u53d8\u6d4b\u5ea6\u548c\u7a81\u53d8\u6982\u7387<\/span><\/strong><\/span><\/h3>\n

8. <\/span><\/strong>\u57fa\u4e8e\u4e3b\u4f53\u6a21\u578b\u7684\u7a81\u53d8\u8def\u5f84\u7edf\u8ba1\u5206\u6790<\/span><\/strong><\/span><\/h3>\n

9. <\/span><\/strong>\u901a\u8fc7\u6709\u9488\u5bf9\u6027\u7684\u793e\u4f1a\u758f\u79bb\u79fb\u52a8\u6d41\u884c\u75c5\u7684\u4e34\u754c\u70b9<\/span><\/strong><\/span><\/h3>\n

1<\/span><\/strong>0. <\/strong>\u6291\u5236\u566a\u58f0\u5f15\u8d77\u7684\u4e34\u754c\u8fc7\u6e21\uff1a\u7ebf\u6027\u589e\u5f3a\u65b9\u6cd5<\/strong><\/span><\/span><\/h3>\n

11. <\/strong>\u877e\u8788\u95ea\u70c1\u89c6\u89c9\u540c\u6b65\u500d\u5468\u671f\u4e34\u754c\u51cf\u901f\u6307\u6807<\/strong><\/span><\/h3>\n
12. \u4e24\u5c42\u7f51\u7edc\u4e0a\u591a\u8def\u590d\u7528\u5f15\u8d77\u7684\u7a81\u53d8<\/span><\/strong><\/span><\/section>\n
13. \u54e5\u672c\u54c8\u6839\u7f51\u7edc\u7814\u7a76\u4e2d\u63a2\u7d22\u793e\u4f1a\u4f20\u67d3\u7684\u5242\u91cf-\u53cd\u5e94\u51fd\u6570\u548c\u66ff\u4ee3\u6a21\u578b<\/span><\/strong><\/span><\/section>\n
14. <\/strong><\/span>\u5806\u80a5\u70b8\u5f39<\/span><\/strong><\/span>\u5728\u8fde\u7eed\u6781\u9650\u4e2d\u7684\u4e0d\u7a33\u5b9a\u6027<\/span><\/strong><\/span><\/section>\n
15. \u57fa\u4e8e\u536b\u661f\u548c\u89c2\u6d4b\u6570\u636e\u7684\u76c6\u5730\u964d\u6c34\u7f51\u7edc\u63a2\u6d4b<\/span><\/strong><\/span><\/section>\n
16. \u7528\u53cc\u6d41\u4f53\u91cf\u5b50\u6d41\u4f53\u529b\u5b66\u6a21\u578b\u7814\u7a76\u78c1\u5316\u91cf\u5b50\u7b49\u79bb\u5b50\u4f53\u4e2d\u5c18\u57c3\u58f0\u6ce2\u7684\u591a\u7ef4\u4e0d\u7a33\u5b9a\u6027<\/span><\/strong><\/span><\/section>\n
17. \u566a\u58f0\u5bf9\u78c1\u611f\u5e94\u53ef\u6fc0\u4ecb\u8d28\u4e2d\u6ce2\u4f20\u64ad\u7684\u5f71\u54cd<\/span><\/strong><\/span><\/section>\n
18. \u5728\u6bd4\u4f8b\u4f9d\u8d56\u7684\u7fa4\u843d\u52a8\u529b\u5b66\u6a21\u578b\u4e2d\u52a0\u5165\u5916\u90e8\u566a\u58f0\uff0c\u53ea\u6709\u6a21\u62df\u7269\u79cd\u624d\u80fd\u751f\u5b58<\/span><\/strong><\/span><\/section>\n
19. \u6709\u9650\u89c4\u6a21\u6548\u5e94\u3001\u4eba\u53e3\u7edf\u8ba1\u566a\u58f0\u4ee5\u53ca\u751f\u6001\u7cfb\u7edf\u52a8\u529b\u5b66<\/span><\/strong><\/span><\/section>\n
20. \u5229\u7528\u903b\u8f91\u64cd\u4f5c\u7684\u4e34\u754c\u70b9<\/span><\/strong><\/span><\/section>\n

21. \u70ed\u58f0\u7cfb\u7edf\u4e2d\u7684\u4e34\u754c\u8f6c\u53d8\u53ca\u5176\u9884\u8b66\u4fe1\u53f7<\/strong><\/span><\/h3>\n


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\u4f5c\u8005\uff1aG. Ambika\uff0cJ\u00fcrgen Kurths<\/span><\/p>\n

\u539f\u6587\u5730\u5740\uff1ahttps:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00281-z<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6b63\u5982\u6211\u4eec\u6240\u77e5\uff0c\u590d\u6742\u7cfb\u7edf\u5927\u591a\u662f\u7531\u51e0\u4e2a\u76f8\u4e92\u4f5c\u7528\u7684\u5b50\u7cfb\u7edf\u7ec4\u6210\u7684\uff0c\u5e76\u4e14\u5f80\u5f80\u62e5\u6709\u591a\u4e2a\u81ea\u7531\u5ea6\u3002\u8fd9\u4e9b\u7cfb\u7edf\u7684\u590d\u6742\u6027\u6765\u81ea\u4e8e\u5b50\u7cfb\u7edf\u76f8\u4e92\u4f5c\u7528\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u3001\u5b50\u7cfb\u7edf\u76f8\u4e92\u4f5c\u7528\u6a21\u5f0f\u7684\u5f02\u8d28\u6027\u4ee5\u53ca\u5b50\u7cfb\u7edf\u52a8\u529b\u5b66\u4e2d\u591a\u65f6\u95f4\u5c3a\u5ea6\u7684\u5b58\u5728\u3002\u8fd9\u7c7b\u7cfb\u7edf\u4e2d\u5178\u578b\u7684\u4f8b\u5b50\u6709\u690d\u88ab\u4e0e\u6e56\u6cca\u76f8\u8fde\u63a5\u7684\u6591\u5757\u3001\u76f8\u4e92\u4f5c\u7528\u7684\u591a\u6c14\u5019\u56e0\u7d20\u3001\u591a\u5c3a\u5ea6\u4e0b\u7684\u57fa\u7840\u8bbe\u65bd\u7cfb\u7edf\u3001\u6df7\u5408\u80fd\u6e90\u7cfb\u7edf\u7b49\u3002\u8fd9\u79cd\u7cfb\u7edf\u53ef\u4ee5\u7528\u591a\u7a33\u5b9a\u5b50\u7cfb\u7edf\u8026\u5408\u7684\u590d\u6742\u7f51\u7edc\u6846\u67b6[8]\u8fdb\u884c\u5efa\u6a21\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e00\u4e2a\u5b50\u7cfb\u7edf\u4e2d\u7684\u7a81\u53d8\u53ef\u80fd\u5bfc\u81f4\u6574\u4e2a\u7cfb\u7edf[9]\u4e2d\u7684\u7a81\u53d8\u7ea7\u8054\u3002\u7136\u540e\uff0c\u901a\u8fc7\u8bc6\u522b\u65e9\u671f\u9884\u8b66\u4fe1\u53f7\u548c\u5236\u5b9a\u6cbb\u7406\u548c\u9884\u9632\u7ea7\u8054\u6548\u5e94\u7684\u7b56\u7565\u6765\u9884\u6d4b\u8fd9\u79cd\u7a81\u53d8\u5c31\u53d8\u5f97\u8feb\u5728\u7709\u776b\u3002\u6b64\u5916\uff0c\u66f4\u5927\u89c4\u6a21\u7684\u5b9e\u8bc1\u548c\u5efa\u6a21\u5de5\u4f5c\uff0c\u4ee5\u4e86\u89e3\u5982\u4f55\u5229\u7528\u793e\u4f1a\u7a81\u53d8\u4e3a\u5168\u7403\u5229\u76ca\u670d\u52a1(\u5982\u51cf\u7f13\u6c14\u5019\u53d8\u5316)\u7684\u6f5c\u529b\uff0c\u4e5f\u662f\u540c\u7b49\u91cd\u8981\u7684\u9700\u6c42\u3002<\/span><\/p>\n


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\u5728\u590d\u6742\u7cfb\u7edf\u4e2d\uff0c\u7531\u4e8e\u5206\u5c94\u3001\u4e34\u754c\u72b6\u6001\u9644\u8fd1\u7684\u6ce2\u52a8\u6216\u566a\u58f0\uff0c\u4ee5\u53ca\u52a8\u529b\u5b66\u63a7\u5236\u53c2\u6570\u7684\u901f\u7387\u53d8\u5316\uff0c\u4f1a\u8bf1\u53d1\u7cfb\u7edf\u7684\u7a81\u53d8<\/span>\uff08the tipping\uff09<\/span>\u3002\u6b64\u5916\uff0c\u8ff7\u5bab\u822c\u7684\u5438\u5f15\u76c6<\/span>\uff08riddled-like basins of attraction\uff09<\/span>\u3001\u5206\u5f62\u8bf1\u5bfc\u7684\u7a81\u53d8\u3001\u8fde\u63a5\u6216\u4ea4\u4e92\u7684\u62d3\u6251\u590d\u6742\u6027\u7b49\u88ab\u8ba4\u4e3a\u662f\u5bfc\u81f4\u4e34\u754c\u8f6c\u53d8\u7684\u56e0\u7d20[10,11]\u3002\u5728\u7a81\u53d8\u53d1\u751f\u7684\u6240\u6709\u673a\u5236\u6216\u8fc7\u7a0b\u4e2d\uff0c\u8bf1\u5bfc\u56e0\u7d20\u7684\u4f5c\u7528\u53ca\u5176\u76f8\u5173\u7684\u7f29\u653e\u73b0\u8c61\u662f\u5f53\u524d\u7814\u7a76\u7684\u70ed\u70b9\u3002\u5728\u8fd9\u65b9\u9762\uff0c\u6c14\u5019\u548c\u73af\u5883\u79d1\u5b66\u3001\u6d41\u884c\u75c5\u3001\u4e34\u5e8a\u7814\u7a76\u548c\u793e\u4f1a\u7ecf\u6d4e\u7b49\u4e0d\u540c\u9886\u57df\u4e2d\u53d1\u751f\u7684\u5173\u4e8e\u7a81\u53d8\u7684\u6848\u4f8b\u7814\u7a76\u975e\u5e38\u5177\u6709\u8bf4\u660e\u6027\u548c\u4fe1\u606f\u6027\u3002<\/span><\/p>\n


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\u672c\u671f\u7279\u520a\u517121\u7bc7\u6587\u7ae0\uff0c\u4ecb\u7ecd\u4e86\u590d\u6742\u7cfb\u7edf\u7a81\u53d8\u7814\u7a76\u7684\u6700\u65b0\u8d8b\u52bf\u548c\u65b9\u5411\uff0c\u4ee5\u53ca\u8be5\u9886\u57df\u9762\u4e34\u7684\u7d27\u8feb\u6311\u6218\u548c\u672a\u6765\u5c55\u671b\u3002\u7814\u7a76\u8005\u5c06\u4ece\u7a81\u53d8\u7684\u673a\u5236\u6216\u8fc7\u7a0b\uff0c\u4ee5\u53ca\u5982\u4f55\u5e94\u5bf9\u7a81\u53d8\u7684\u5bf9\u7b56\u51fa\u53d1\uff0c\u7ee7\u7eed\u7814\u7a76\u7a81\u53d8\u7684\u63a7\u5236\uff0c\u6700\u7ec8\u4ee5\u4e0d\u540c\u7684\u9886\u57df\u548c\u5e94\u7528\u7684\u6848\u4f8b\u7814\u7a76\u7ed3\u675f\u3002<\/span><\/p>\n


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\u524d\u516d\u7bc7\u6587\u7ae0\u805a\u7126\u4e8e\u8bf1\u53d1\u7a81\u53d8\u7684\u673a\u5236\u3002Gowthaman\u7b49\u4eba\u7684[12]\u62a5\u544a\u4e86\u5bf9\u79f0\u7834\u7f3a\u8026\u5408\u548c\u975e\u5747\u5300\u6027\u7a0b\u5ea6\u4e4b\u95f4\u7684\u7ade\u4e89\u76f8\u4e92\u4f5c\u7528\u5982\u4f55\u51b3\u5b9a\u8026\u5408Stuart-Landau\u632f\u5b50\u7cfb\u7edf\u7684\u6d8c\u73b0\u52a8\u529b\u5b66<\/span>\uff08emergent dynamics\uff09<\/span>\uff0c\u5e76\u968f\u7740\u975e\u5747\u5300\u6027\u7684\u589e\u52a0\u5bfc\u81f4\u5206\u5c94\u8bf1\u5bfc\u7684\u7a81\u53d8\u8fdb\u5165\u8001\u5316\u72b6\u6001\u3002Mueller\u7b49\u4eba[13]\u7814\u7a76\u4e86\u9884\u671f<\/span>\uff08anticipation\uff09<\/span>\u5982\u4f55\u5728\u4e2a\u4f53\u7684\u793e\u4f1a\u7f51\u7edc\u4e0e\u6c61\u67d3\u7b49\u81ea\u7136\u52a8\u6001\u73af\u5883\u7cfb\u7edf\u4e4b\u95f4\u53d1\u6325\u4e2d\u4ecb\u4f5c\u7528\u8fd9\u4e00\u91cd\u8981\u95ee\u9898\u3002\u4ed6\u4eec\u53d1\u73b0\uff0c\u793e\u4f1a\u53d8\u5316\u53ef\u4ee5\u7a33\u5b9a\u73af\u5883\uff0c\u9632\u6b62\u6f5c\u5728\u7684\u793e\u4f1a\u751f\u6001\u5d29\u6e83\u3002\u6b63\u5982Verma\u548cAmbika[14]\u6240\u793a\uff0c\u7531\u4e8e\u4e0e\u53e6\u4e00\u4e2a\u7cfb\u7edf\u7f51\u7edc\u7684\u591a\u8def\u590d\u7528\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u4e00\u7ec4\u7cfb\u7edf\u4e2d\u7684\u7a81\u53d8\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8026\u5408\u62d3\u6251\u4f1a\u5f71\u54cd\u8fd9\u4e24\u4e2a\u591a\u8def\u590d\u7528\u5c42\u4e0a\u7684\u8fc7\u6e21\u7684\u6027\u8d28\u3002Asir\u7b49\u4eba\u63d0\u51fa\u4e86\u5728\u5404\u79cd\u751f\u7269\u548c\u5316\u5b66\u7cfb\u7edf\u4e2d\uff0c\u52a8\u6001\u7fa4\u4f53\u611f\u5e94\u5982\u4f55\u5bfc\u81f4\u5411\u7a33\u6001\u7684\u4e0d\u8fde\u7eed\u8fc7\u6e21\u3002\u5728Arumugam\u7b49\u4eba[16]\u7684\u6587\u7ae0\u91cc\uff0c\u7814\u7a76\u8005\u770b\u5230\u5728\u7a7a\u95f4\u8026\u5408\u7684\u751f\u6001\u7cfb\u7edf\u4e2d\uff0c\u901f\u7387\u8bf1\u5bfc\u7684\u7a81\u53d8\u5bfc\u81f4\u4e86\u4e00\u4e2a\u5143\u7fa4\u843d\u7684\u706d\u7edd\u3002\u5728\u566a\u58f0\u4ecb\u5bfc\u7684\u8fc7\u6e21\u7684\u80cc\u666f\u4e0b\uff0cCabrera\u7b49\u4eba\u62a5\u544a\u4e86\u4e00\u9879\u5173\u4e8e\u566a\u58f0\u4ecb\u5bfc\u7684\u8fc7\u6e21\u7684\u7814\u7a76\uff0c\u8be5\u7814\u7a76\u663e\u793a\u4e86\u5982\u4f55\u901a\u8fc7\u63a5\u8fd1\u7a33\u5b9a\u8fb9\u754c\u7684\u786e\u5b9a\u6027\u548c\u968f\u673a\u65f6\u95f4\u5c3a\u5ea6\u4e4b\u95f4\u7684\u8026\u5408\u4ecb\u5bfc\u8fc7\u7a0b\u4ee5\u907f\u514d\u7184\u706d\u8f6c\u53d8<\/span>\uff08extinguishing transition\uff09<\/span>\u3002<\/span><\/p>\n


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\u63a5\u4e0b\u6765\uff0c\u51e0\u7bc7\u6587\u7ae0\u4ecb\u7ecd\u4e86\u5173\u4e8e\u7a81\u53d8\u73b0\u8c61\u7279\u5f81\u7684\u6d4b\u91cf\u65b9\u6cd5\u3002Ashwin\u548cNewman[18]\u7684\u7814\u7a76\u662f\u57fa\u4e8e\u7a81\u53d8\u6982\u7387\u6765\u91cf\u5316\u6df7\u6c8c\u5438\u5f15\u5b50\u4e4b\u95f4\u7684\u901f\u7387\u4f9d\u8d56\u7a81\u53d8\u3002Helfmann\u7b49\u4eba[19]\u8ba8\u8bba\u4e86\u57fa\u4e8e\u4e3b\u4f53<\/span>\uff08agent\uff09<\/span>\u6a21\u578b\u4e2d\u76f8\u5173\u5b50\u96c6\u548c\u8def\u5f84\u4e4b\u95f4\u7684\u566a\u58f0\u8bf1\u53d1\u7a81\u53d8\u3002\u4f7f\u7528\u4e24\u4e2a\u6a21\u578b\uff0c\u4ed6\u4eec\u7528\u8f6c\u79fb\u8def\u5f84\u7406\u8bba\u6765\u8bba\u8bc1\u7a81\u53d8\u884c\u4e3a\uff0c\u8be5\u7406\u8bba\u7ed9\u51fa\u4e86\u7a81\u53d8\u8def\u5f84\u7684\u7edf\u8ba1\u7406\u89e3\u3002\u4e0b\u4e00\u7bc7\u6587\u7ae0\u5c06\u8ba8\u8bba\u63a7\u5236\u7a81\u53d8\u7684\u7b56\u7565\uff0c\u8fd9\u4e0e\u907f\u514d\u8f6c\u53d8\u5e26\u6765\u4e0d\u826f\u6216\u6709\u5bb3\u540e\u679c\u6709\u5173\u3002Ma\u7b49\u4eba\u7684[20]\u63d0\u51fa\u4e86\u4e00\u4e2a\u65b0\u7684\u89c6\u89d2\uff0c\u901a\u8fc7\u5916\u90e8\u7ebf\u6027\u589e\u5f3a\u65b9\u6cd5\u6291\u5236\u566a\u58f0\u5f15\u8d77\u7684\u4ece\u7406\u60f3\u72b6\u6001\u5230\u53e6\u4e00\u79cd\u5bf9\u6bd4\u72b6\u6001\u7684\u4e34\u754c\u8fc7\u6e21\uff0c\u5e76\u6f14\u793a\u4e86\u53cc\u7a33\u6001\u548c\u4e09\u7a33\u6001\u7cfb\u7edf\u7684\u65b9\u6cd5\u3002\u5728Ansari et al.[21]\u7684\u6587\u7ae0\u4e2d\uff0c\u7814\u7a76\u8005\u91c7\u7528\u9a6c\u5c14\u53ef\u592b\u94fe\u2014\u8499\u7279\u5361\u7f57\u65b9\u6cd5\uff0c\u901a\u8fc7\u51cf\u5c11\u793e\u4f1a\u4ea4\u5f80\u90bb\u63a5\u77e9\u9635\u7684\u6700\u5927\u7279\u5f81\u503c\u6765\u79fb\u52a8\u6d41\u884c\u75c5\u7a81\u53d8\u70b9\u3002\u5229\u7528SIS\/SIR\u6a21\u578b\uff0c\u8be5\u6587\u7ae0\u8868\u660e\u4ece\u6d41\u884c\u75c5\u72b6\u6001\u5230\u975e\u6d41\u884c\u75c5\u72b6\u6001\u7684\u8f6c\u53d8\u53d1\u751f\u5728\u8fd9\u79cd\u7a0b\u5ea6\u5747\u8d28\u7f51\u7edc<\/span>\uff08degree-homogenized networks\uff09<\/span>\u4e2d\u3002<\/span><\/p>\n


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\u63a5\u4e0b\u6765\uff0c\u7814\u7a76\u8005\u5c06\u5bf9\u4e0d\u540c\u9886\u57df\u7684\u7a81\u53d8\u53ca\u76f8\u5173\u73b0\u8c61\u8fdb\u884c\u5177\u4f53\u7684\u6848\u4f8b\u7814\u7a76\uff1aClarke \u7b49\u4eba\u7684\u8fde\u7eed\u6781\u9650\u4e2d\u7684\u5806\u80a5\u70b8\u5f39\u4e0d\u7a33\u5b9a\u6027[22]\u3002\u4ea4\u901a\u6d41\u7cfb\u7edf\u6a21\u578b\u4e2d\u7684\u6781\u7aef\u4e8b\u4ef6\uff0cGupta \u548c Santhanam [23]\uff0c\u54e5\u672c\u54c8\u6839\u7f51\u7edc\u4e2d\u793e\u4f1a\u4f20\u67d3\u7684\u4f20\u64ad\u8fc7\u7a0b\uff0cDonges \u7b49\u4eba[24]\u3002\u877e\u8788\u95ea\u70c1\u89c6\u89c9\u7684\u4e25\u91cd\u51cf\u6162\uff0cMehrabbeik \u7b49\u4eba[25]\u3002\u6765\u81ea\u536b\u661f\u6570\u636e\u7684\u76c6\u5730\u964d\u6c34\uff0cGadhawe \u7b49\u4eba[26]\u3002\u5c18\u57c3\u58f0\u6ce2\u7684\u4e0d\u7a33\u5b9a\u6027\uff0cGao \u548c Wu [27]\uff0c\u53ef\u6fc0\u53d1\u4ecb\u8d28\u4e2d\u7684\u6ce2\u4f20\u64ad\uff0cRamakrishnan \u7b49\u4eba [28]\uff0c\u7fa4\u843d\u52a8\u529b\u5b66\u4e2d\u7684\u62df\u6001\u7269\u79cd\uff0cGarain [29]\uff0c\u4ee5\u53ca\u6709\u9650\u5c3a\u5bf8\u6548\u5e94\u548c\u4eba\u53e3\u566a\u58f0\u751f\u6001\u7cfb\u7edf\u52a8\u529b\u5b66\uff0cMajumder \u7b49\u4eba [30]\u3002<\/span><\/p>\n


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\u6700\u540e\uff0c\u7814\u7a76\u8005\u7b80\u8981\u56de\u987e\u4e86\u8fd9\u4e9b\u7a81\u53d8\u5728\u4e24\u79cd\u4e0d\u540c\u60c5\u51b5\u4e0b\u7684\u5e94\u7528\u3002\u4e00\u4e2a\u6709\u8da3\u7684\u5e94\u7528\u662f\u5229\u7528\u903b\u8f91\u64cd\u4f5c[31]\u7684\u7a81\u53d8\u70b9\uff0c\u8fd9\u6837\u7a81\u53d8\u673a\u5236\u5c31\u53ef\u4ee5\u7528\u4e8e\u6784\u9020\u901a\u7528\u8ba1\u7b97\u8bbe\u5907\u3002\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u4e34\u754c\u70b9\u80fd\u591f\u5728\u53c2\u6570\u7684\u5fae\u5c0f\u53d8\u5316\u4e0b\u5728\u975e\u5e38\u4e0d\u540c\u7684\u5438\u5f15\u5b50\u4e4b\u95f4\u5207\u6362\uff0c\u8fd9\u53ef\u88ab\u5229\u7528\u9ad8\u6548\u548c\u7075\u6d3b\u5730\u5b9e\u73b0\u57fa\u672c\u903b\u8f91\u64cd\u4f5c\uff0c\u5176\u53ef\u9760\u6027\u901a\u8fc7\u9002\u5ea6\u7684\u566a\u58f0\u5f97\u5230\u589e\u5f3a\u3002Pavithran \u7b49\u4eba\u56de\u987e\u4e86\u68c0\u6d4b\u70ed\u58f0\u7cfb\u7edf\u4e2d\u7684\u632f\u8361\u4e0d\u7a33\u5b9a\u6027\u6240\u9762\u4e34\u7684\u6311\u6218\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u4ece\u6df7\u6c8c\u72b6\u6001\u5230\u901a\u8fc7\u95f4\u6b47\u72b6\u6001\u7684\u6781\u9650\u5faa\u73af\u7684\u8fc7\u6e21\u3002\u8fd9\u7bc7\u7efc\u8ff0\u8fd8\u5f3a\u8c03\u4e86\u7a33\u5b9a\u8fd0\u884c\u671f\u95f4\u7cfb\u7edf\u4e2d\u5b58\u5728\u7684\u56fa\u6709\u6ce2\u52a8\u5982\u4f55\u7528\u4e8e\u5b9e\u65f6\u63d0\u4f9b\u8b66\u544a\uff0c\u4ee5\u4fbf\u542f\u52a8\u63a7\u5236\u63aa\u65bd\u4ee5\u51cf\u8f7b\u5173\u952e\u8fc7\u6e21\u7684\u5f71\u54cd\u3002<\/span><\/p>\n


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\u7814\u7a76\u8005\u6ce8\u610f\u5230\uff0c\u590d\u6742\u7cfb\u7edf\u4e2d\u4e0e\u7a81\u53d8\u76f8\u5173\u7684\u7814\u7a76\u6b63\u65e5\u6e10\u53d7\u5230\u6570\u636e\u9a71\u52a8\uff0c\u8fd9\u4e3b\u8981\u662f\u7531\u4e8e\u6240\u6d89\u53ca\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\u7684\u590d\u6742\u6027\u548c\u4e0d\u5b8c\u5168\u7406\u89e3\u3002\u56e0\u6b64\uff0c\u672a\u6765\u7684\u53d1\u5c55\u8d8b\u52bf\u662f\u5c06\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u3001\u81ea\u9002\u5e94\u591a\u5c42\u7f51\u7edc\u548c\u673a\u5668\u5b66\u4e60\u7ed3\u5408\u5728\u4e00\u8d77\uff0c\u4ee5\u5b9e\u73b0\u5168\u9762\u548c\u6709\u6548\u7684\u7ed3\u679c\u3002<\/span><\/p>\n


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1. \u5bf9\u79f0\u7834\u574f\u5f15\u8d77\u7684\u7a81\u53d8\u8001\u5316<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/h3>\n

Symmetry-breaking-induced tipping to aging<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00010-6<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u7814\u7a76\u4e86N\u4e2a\u5168\u5c40\u8026\u5408Stuart-Landau\u632f\u5b50\u7cfb\u7edf\u4e2d\uff0c\u975e\u5747\u5300\u8026\u5408\u548c\u5bf9\u79f0\u7834\u7f3a\u8026\u5408\u5bf9\u7cfb\u7edf\u4e2d\u51fa\u73b0\u52a8\u529b\u5b66\u7684\u7ade\u4e89\u6548\u5e94\u3002\u901a\u8fc7\u589e\u52a0\u975e\u5747\u5300\u6027\uff0c\u7814\u7a76\u8005\u5229\u7528Hopf\u5206\u5c94\u53c2\u6570\u7684\u6807\u51c6\u5dee\uff0c\u53d1\u73b0\u5bf9\u4e8e\u5bf9\u79f0\u7834\u7f3a\u8026\u5408\uff0c\u5f53\u8026\u5408\u503c\u8f83\u4f4e\u65f6\uff0c\u66f4\u503e\u5411\u4e8e\u5b8f\u89c2\u632f\u8361\uff0c\u5bf9\u4e8e\u8026\u5408\u503c\u8f83\u5927\u65f6\uff0c\u66f4\u503e\u5411\u4e8e\u975e\u5747\u5300\u7a33\u6001\u3002\u4ece\u5b8f\u89c2\u632f\u8361\u72b6\u6001\u5230\u5747\u5300\u7a33\u5b9a\u72b6\u6001<\/span>\uff08\u8001\u5316\u72b6\u6001\uff09<\/span>\u4e5f\u6709\u4e00\u4e2a\u8fc7\u6e21\uff0c\u5373\u7a81\u53d8\u3002\u5373\u4f7f\u7f51\u7edc\u4e2d\u5b58\u5728\u5927\u91cf\u7684\u975e\u6d3b\u8dc3\u632f\u8361\u5b50\uff0c\u6269\u6563\u8026\u5408\u4e2d\u7684\u9650\u5236\u56e0\u7d20\u4e5f\u6709\u5229\u4e8e\u7f51\u7edc\u7684\u5b8f\u89c2\u632f\u8361\u72b6\u6001\uff0c\u4ece\u800c\u63d0\u9ad8\u4e86\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u3002<\/span><\/p>\n


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\u5bf9\u4e8e a = -0.50 \u548c\u4e24\u4e2a\u4e0d\u540c\u7684\u56fa\u6709\u9891\u7387\u503c\uff0c\u4f7f\u7528 XPPAUT \u4f5c\u4e3a\u8026\u5408\u5f3a\u5ea6\u51fd\u6570\u7684\u5206\u5c94\u56fe\u3002a \u03c9=0.1\uff0cb \u03c9=0.2\u3002\u5b9e\u5fc3\u5706\u548c\u5b9e\u7ebf\u5bf9\u5e94\u4e8e\u7a33\u5b9a\u7684\u6781\u9650\u73af\u632f\u8361\u548c\u7a33\u5b9a\u7684\u7a33\u6001\uff0c\u800c\u7a7a\u5fc3\u5706\u548c\u865a\u7ebf\u5bf9\u5e94\u4e8e\u4e0d\u7a33\u5b9a\u7684\u6781\u9650\u73af\u632f\u8361\u548c\u4e0d\u7a33\u5b9a\u7684\u7a33\u6001<\/span><\/section>\n


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\u7814\u7a76\u8005\u5229\u7528\u81ea\u6d3d\u573a\u65b9\u6cd5\u5c06\u5168\u5c40\u8026\u5408\u632f\u5b50\u7b80\u5316\u4e3a\u4e24\u4e2a\u5b8f\u89c2\u9636\u53c2\u91cf\u7684\u6f14\u5316\u65b9\u7a0b\u7cfb\u7edf\uff0c\u5b8f\u89c2\u9636\u53c2\u91cf\u5bf9\u5e94\u4e8e\u5e73\u5747\u573a\u548c\u5f62\u72b6\u53c2\u6570\u3002\u7531\u5e73\u5747\u573a\u53d8\u91cf\u5f97\u5230\u7684\u5206\u5c94\u56fe\u9610\u660e\u4e86N\u4e2a\u5168\u5c40\u8026\u5408Stuart-Landau\u632f\u5b50\u4e2d\u89c2\u6d4b\u5230\u7684\u52a8\u6001\u8dc3\u8fc1\u7684\u5404\u79cd\u5206\u5c94\u60c5\u5f62\u3002\u7279\u522b\u662f\uff0c\u901a\u8fc7Hopf\u548c\u5e72\u8349\u53c9\u5206\u5c94\u53d1\u73b0\u4e86\u5411\u8001\u5316\u72b6\u6001\u503e\u659c\u7684\u73b0\u8c61\uff0c\u8bf4\u660e\u4e86\u5206\u5c94\u8bf1\u5bfc\u7684\u503e\u659c\u73b0\u8c61\u3002\u7531\u5e73\u5747\u573a\u53d8\u91cf\u63a8\u5bfc\u51fa\u7684\u8fd9\u4e9b\u5206\u5c94\u7684\u89e3\u6790\u7a33\u5b9a\u6027<\/span>\uff08\u4e34\u754c\uff09<\/span>\u66f2\u7ebf\u4e0e\u4eff\u771f\u7ed3\u679c\u76f8\u5f53\u543b\u5408\u3002<\/span><\/p>\n


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2. \u9884\u671f\u8bf1\u53d1\u7684\u793e\u4f1a\u503e\u5411\u6027\uff1a<\/strong><\/strong><\/p>\n

\u793e\u4f1a\u52a8\u529b\u5b66\u80fd\u7a33\u5b9a\u73af\u5883\u5417\uff1f<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/h3>\n

Anticipation-induced social tipping: can the environment be stabilised by social dynamics?<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00011-5<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5728\u8fc7\u53bb\u7684\u51e0\u5341\u5e74\u91cc\uff0c\u4eba\u7c7b\u6d3b\u52a8\u5bfc\u81f4\u4e86\u5168\u7403\u5730\u7403\u7cfb\u7edf\u7684\u53d8\u5316\uff0c\u4f8b\u5982\u6c14\u5019\u53d8\u5316\u6216\u751f\u7269\u591a\u6837\u6027\u7684\u4e27\u5931\u3002\u540c\u65f6\uff0c\u8fd9\u4e9b\u76f8\u5173\u5f71\u54cd\u63d0\u9ad8\u4e86\u5168\u7403\u793e\u4f1a\u7684\u73af\u5883\u610f\u8bc6\uff0c\u4ece\u800c\u5bfc\u81f4\u793e\u4f1a\u548c\u81ea\u7136\u5730\u7403\u7cfb\u7edf\u4e4b\u95f4\u7684\u52a8\u6001\u53cd\u9988\u3002\u73b0\u4ee3\u7684\u5730\u7403\u7cfb\u7edf\u52a8\u529b\u5b66\u5efa\u6a21\u5c1d\u8bd5\u5f88\u5c11\u5305\u542b\u8fd9\u6837\u7684\u5171\u540c\u6f14\u5316\u548c\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u7c7b\u5efa\u6a21\u5927\u591a\u6570\u662f\u901a\u8fc7\u76f4\u63a5\u6216\u8bb0\u5fc6\u8fc7\u53bb\u7684\u5f71\u54cd\u8fdb\u884c\u5355\u5411\u7814\u7a76\u3002<\/span><\/p>\n


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\u6a21\u578b\u8bbe\u7f6e\u7684\u793a\u610f\u56fe\uff1a\u73af\u5883\u4ec5\u7531\u4e00\u4e2a\u53d8\u91cf\u8868\u793a\uff0c\u5373\u5168\u7403\u6c61\u67d3\u6c34\u5e73 Y\uff0c\u5176\u53d8\u5316\u4e0e\u5176\u81ea\u8eab\u7684\u503c\u6210\u6b63\u6bd4\uff0c\u7cfb\u7edf\u7684\u5e73\u5747\u72b6\u6001\u662f\u6c61\u67d3\u56e0\u5b50 X \u7684\u4efd\u989d\u3002\u793e\u4f1a\u7cfb\u7edf\u7531\u4e2a\u4f53\u4e3b\u4f53\u7ec4\u6210\uff0c\u8fd9\u4e9b\u4e3b\u4f53\u8981\u4e48\u589e\u52a0\u6c61\u67d3\uff0c\u8981\u4e48\u53cd\u4e4b\u3002\u4ed6\u4eec\u6839\u636e\u5f53\u524d\u7684\u6c61\u67d3\u6c34\u5e73\uff08\u76f4\u63a5\u5f71\u54cd\uff09\u3001\u672a\u6765\u9884\u671f\u7684\u6c61\u67d3\u6c34\u5e73\uff08\u9884\u671f\u5f71\u54cd\uff09\u548c\u4ed6\u4eec\u5728\u7f51\u7edc\u4e2d\u7684\u76f4\u63a5\u90bb\u5c45\u7684\u884c\u4e3a\uff08\u793e\u4f1a\u4f20\u67d3\uff09\u6765\u6539\u53d8\u4ed6\u4eec\u7684\u4e8c\u5143\u72b6\u6001 xi<\/span><\/section>\n


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\u8ba4\u8bc6\u5230\u793e\u4f1a\u5177\u6709\u989d\u5916\u7684\u9884\u89c1\u80fd\u529b\u4e4b\u540e\uff0c\u672c\u5de5\u4f5c\u63d0\u51fa\u4e86\u4e00\u4e2a\u793e\u4f1a\u2014\u751f\u6001\u534f\u540c\u8fdb\u5316\u7684\u6982\u5ff5\u53cd\u9988\u6a21\u578b\uff0c\u5176\u4e2d\uff0c\u7814\u7a76\u8005\u6784\u5efa\u4e86\u201c\u9884\u671f\u201d\u4ee5\u4f5c\u4e3a\u793e\u4f1a\u548c\u81ea\u7136\u7cfb\u7edf\u4e4b\u95f4\u7684\u4e2d\u4ecb\u3002\u7814\u7a76\u8005\u7684\u6a21\u578b\u53c2\u8003\u4e86\u8fc7\u53bb\u793e\u4f1a\u5b66\u53cc\u7a33\u5b9a\u6027\u9608\u503c\u6a21\u578b\u7684\u7ed3\u679c\uff0c\u5047\u5b9a\u4e00\u4e2a\u9759\u6001\u73af\u5883\u3002\u4e00\u65e6\u73af\u5883\u56e0\u793e\u4f1a\u884c\u4e3a\u800c\u53d1\u751f\u53d8\u5316\uff0c\u7cfb\u7edf\u5c31\u4f1a\u8f6c\u800c\u8d8b\u540c\u4e8e\u4e00\u4e2a\u5168\u7403\u7a33\u5b9a\u7684\u3001\u4f46\u4e0d\u4e00\u5b9a\u662f\u4eba\u4eec\u6240\u671f\u671b\u7684\u5438\u5f15\u5b50<\/span>\uff08attractor\uff09<\/span>\u3002\u6700\u7ec8\uff0c\u7814\u7a76\u8005\u9610\u660e\uff0c\u5bf9\u672a\u6765\u751f\u6001\u72b6\u6001\u7684\u9884\u671f\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u7684\u4e9a\u7a33\u6001\uff0c\u5728\u90a3\u91cc\uff0c\u6240\u671f\u671b\u7684\u72b6\u6001\u53ef\u4ee5\u6301\u7eed\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u8005\u8bc1\u660e\uff0c\u8fdc\u89c1\u548c\u9884\u671f\u5f62\u6210\u4e86\u4e00\u4e2a\u91cd\u8981\u7684\u673a\u5236\uff0c\u4e00\u65e6\u5b83\u7684\u65f6\u95f4\u8303\u56f4\u53d8\u5f97\u8db3\u591f\u5927\uff0c\u5c31\u4f1a\u57f9\u517b\u793e\u4f1a\u503e\u5411\u4e8e\u80fd\u591f\u7a33\u5b9a\u73af\u5883\u548c\u9632\u6b62\u6f5c\u5728\u7684\u793e\u4f1a\u751f\u6001\u5d29\u6e83\u7684\u884c\u4e3a\u3002<\/span><\/p>\n


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3. \u590d\u6742\u7f51\u7edc\u4ea4\u901a\u6d41<\/strong><\/strong><\/p>\n

Nagel-Schreckenberg\u6a21\u578b\u4e2d\u7684\u6781\u7aef\u4e8b\u4ef6<\/strong><\/strong><\/p>\n<\/section>\n

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Extreme events in Nagel\u2013Schreckenberg model of traffic flow on complex networks\uff1a<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00016-0<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u672c\u6587\u5c06Nagel-Schreckenberg\u8f66\u8f86\u4ea4\u901a\u6a21\u578b\u63a8\u5e7f\u5230\u65e0\u6807\u5ea6\u7f51\u7edc\u4e0a\u7684\u8f66\u8f86\u7cfb\u7edf\uff0c\u4ee5\u7814\u7a76\u5176\u4e2d\u7684\u6781\u7aef\u4e8b\u4ef6\u3002\u786e\u5b9a\u4e86\u81ea\u7531\u6d41\u52a8\u72b6\u6001\u548c\u62e5\u6324\u72b6\u6001\u5bf9\u8f66\u8f86\u5bc6\u5ea6\u7684\u4f9d\u8d56\u5173\u7cfb\u3002\u7279\u522b\u662f\u5728\u8f66\u6d41\u5bc6\u5ea6\u8f83\u4f4e\u65f6\uff0c\u8f66\u6d41\u5904\u4e8e\u81ea\u7531\u6d41\u52a8\u72b6\u6001\uff0c\u5728\u8f66\u6d41\u5bc6\u5ea6\u8f83\u9ad8\u65f6\uff0c\u8f66\u6d41\u9010\u6e10\u8fc7\u6e21\u5230\u62e5\u6324\u72b6\u6001\u3002<\/span><\/p>\n


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\u8be5\u56fe\u663e\u793a\u4e86\u5728\u4efb\u610f\u65f6\u95f4\u7531\u7f51\u7edc\u7684 4 \u4e2a\u8282\u70b9\u7ec4\u6210\u7684\u4e00\u5c0f\u90e8\u5206\u3002\u8282\u70b9\u901a\u8fc7\u53cc\u5411\u8fb9\u8fde\u63a5\uff0c\u6bcf\u4e2a\u65b9\u5411\u7531\u4e00\u6761\u8f66\u9053\u7ec4\u6210\u3002\u6bcf\u4e2a\u6cf3\u9053\u662f L \u4e2a\u4f4d\u70b9\u7684\u4e00\u7ef4\u70b9\u9635\uff08\u51fa\u4e8e\u4ee3\u8868\u6027\u76ee\u7684\uff0c\u6b64\u5904 L=18\uff09\u3002\u7ad9\u70b9\u4e0a\u7684\u7ea2\u8272\u5706\u5708\u8868\u793a\u8be5\u7ad9\u70b9\u5b58\u5728\u8f66\u8f86<\/span><\/section>\n


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\u5229\u7528\u975e\u8d8b\u52bf\u6da8\u843d\u5206\u6790\u8868\u660e\uff0c\u5728\u4f4e\u5bc6\u5ea6\u72b6\u6001\u4e0b\uff0c\u8f66\u8f86\u6d41\u91cf\u5177\u6709\u957f\u7a0b\u76f8\u5173\u6027\uff1b\u800c\u5728\u5bc6\u5ea6\u8f83\u9ad8\u65f6\uff0c\u901a\u91cf\u53d8\u5f97\u4e0d\u76f8\u5173\u3002\u7814\u7a76\u8005\u7814\u7a76\u6781\u7aef\u4e8b\u4ef6\u7684\u590d\u53d1\u95f4\u9694\u5206\u5e03\u53ca\u5176\u53d1\u751f\u5728\u4f4e\u548c\u9ad8\u8f66\u8f86\u5bc6\u5ea6\u72b6\u6001\u4e0b\u7684\u6982\u7387\u3002\u7814\u7a76\u8868\u660e\uff0c\u6781\u7aef\u4e8b\u4ef6\u7684\u53d1\u751f\u6982\u7387\u4e0e\u5b9a\u4e49\u6781\u7aef\u4e8b\u4ef6\u7684\u8282\u70b9\u6216\u9608\u503c\u7684\u7a0b\u5ea6\u65e0\u5173\u3002<\/span><\/p>\n


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\u52a8\u6001\u7fa4\u4f53\u611f\u5e94\u5f71\u54cd\u7684\u4e34\u754c\u8f6c\u53d8<\/strong><\/strong><\/p>\n<\/section>\n

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Critical transition influenced by dynamic quorum sensing in nonlinear oscillators<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00012-4<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u57fa\u4e8e\u9608\u503c\u7814\u7a76\u4e86\u975e\u7ebf\u6027\u632f\u5b50\u4e0e\u52a8\u529b\u5b66\u73af\u5883\u76f8\u4e92\u4f5c\u7528\u7684\u4e34\u754c\u8f6c\u53d8\u3002\u9608\u503c\u662f\u7531\u7f51\u7edc\u4e2d\u5b58\u5728\u7684\u5355\u4e2a\u632f\u8361\u5668\u7684\u632f\u5e45\u7f16\u7801\u7684\u3002\u5176\u5173\u952e\u601d\u60f3\u662f\uff0c\u5f53\u632f\u8361\u5668\u7684\u632f\u5e45\u8d85\u8fc7\u9608\u503c\u65f6\uff0c\u8be5\u8282\u70b9\u5c06\u4ee5\u7279\u5b9a\u7684\u76f8\u4e92\u4f5c\u7528\u5f3a\u5ea6\u4e0e\u73af\u5883\u8026\u5408\u3002\u8fd9\u79cd\u8003\u8651\u6a21\u4eff\u4e86\u7fa4\u4f53\u611f\u5e94\u673a\u5236\uff0c\u5f53\u79cd\u7fa4\u5bc6\u5ea6\u8fbe\u5230\u9608\u503c\u65f6\uff0c\u8bb8\u591a\u751f\u7269\u548c\u5316\u5b66\u7cfb\u7edf\u901a\u8fc7\u7fa4\u4f53\u611f\u5e94\u5b9e\u73b0\u96c6\u4f53\u884c\u4e3a\u3002<\/span><\/p>\n


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\u8282\u70b9\u4e4b\u95f4\u7684\u7f51\u7edc\u52a8\u529b\u5b66\u6a21\u578b<\/span><\/p>\n


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\u901a\u8fc7\u4e0a\u8ff0\u7814\u7a76\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\uff1a\u5f53\u9608\u503c\u5c0f\u4e8e\u6700\u5927\u632f\u5e45\u65f6\uff0c\u51fa\u73b0\u4e86\u5411\u7a33\u6001\u7684\u4e00\u9636\u4e0d\u8fde\u7eed\u8f6c\u53d8\u3002\u8be5\u6587\u8fd8\u63a8\u5bfc\u4e86\u5728\u6240\u9009\u6a21\u578b\u4e2d\u83b7\u5f97\u4e34\u754c\u70b9\u7684\u4e00\u822c\u8868\u8fbe\u5f0f\u3002<\/span><\/p>\n


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5. \u7a7a\u95f4\u751f\u6001\u7cfb\u7edf\u4e2d<\/strong><\/strong><\/p>\n

\u901f\u7387\u8bf1\u5bfc\u7684\u7a81\u53d8\u4e0e\u5236\u5ea6\u53d8\u8fc1<\/strong><\/strong><\/p>\n<\/section>\n

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Rate-induced tipping and regime shifts in a spatial ecological system<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00139-4<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u73af\u5883\u53d8\u5316\u7684\u901f\u7387\u5982\u4f55\u5f71\u54cd\u4e00\u4e2a\u751f\u6001\u7fa4\u843d\u7684\u7a33\u5b9a\u6027\u548c\u6301\u4e45\u6027\u3002\u7814\u7a76\u8005\u4f7f\u7528\u7a7a\u95f4\u8026\u5408\u751f\u6001\u7cfb\u7edf\u7684\u73af\u5883\u53c2\u6570\u7684\u663e\u5f0f\u53d8\u5316\u7387\uff0c\u7814\u7a76\u4e0e\u5143\u793e\u533a\u706d\u7edd\u76f8\u5173\u7684\u901f\u7387\u4f9d\u8d56\u6027\u53cd\u5e94\u3002\u7814\u7a76\u8005\u7684\u7814\u7a76\u7ed3\u679c\u9610\u660e\u4e86\u901f\u7387\u8bf1\u5bfc\u7684\u8870\u51cf<\/span>\uff08R-tipping\uff09<\/span>\u7684\u5404\u79cd\u60c5\u51b5\uff0c\u5982\u901a\u8fc7\u589e\u52a0\u632f\u8361\u632f\u5e45\u6765\u5b9e\u73b0\u7684\u7a81\u53d8\u3001\u901a\u8fc7\u540c\u6b65\u52a8\u529b\u5b66\u6765\u5b9e\u73b0\u7684\u7a81\u53d8\u4ee5\u53ca\u901a\u8fc7\u8ddf\u8e2a\u4e0d\u7a33\u5b9a\u72b6\u6001\u6765\u5b9e\u73b0\u7684\u7a81\u53d8\u3002<\/span><\/p>\n


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\u901f\u7387\u4f9d\u8d56\u72b6\u6001\u901a\u8fc7\u8ddf\u8e2a\u4e0d\u7a33\u5b9a\u72b6\u6001\u53d1\u751f\u53d8\u5316\u3002\u5f53 \u03bc = 0 \u65f6\uff0c\u5143\u7fa4\u843d\u5728 HB1 \u548c\u66f4\u9ad8\u7684 K \u503c\u4e0b\u5177\u6709\u591a\u91cd\u7a33\u5b9a\u6027\u3002\u5bf9\u4e8e\u4ee5\u901f\u7387\uff08 \u03bc = -0.0001\uff09\u964d\u4f4e\u627f\u8f7d\u80fd\u529b\uff0c\u4eba\u53e3\u5bc6\u5ea6\u7684\u6f14\u53d8\u663e\u793a\u51fa\u901a\u8fc7\u8ddf\u8e2a\u8de8\u4e34\u754c\u5206\u53c9\uff08TB\uff09\u5904\u7684\u4e0d\u7a33\u5b9a\u72b6\u6001\u7684\u8f6c\u53d8 . \u5728\u8fd9\u91cc\uff0c\u5176\u4ed6\u53c2\u6570\u8bbe\u5b9a\u4e3a r=0.6, Dv=0, Dh=0.3, Q1=0, Q2=0.8, a=-0.4, \u03b1=0.8, b=0.2, \u03b2=0.5, and m=0.16<\/span><\/section>\n


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\u6b64\u5916\uff0c\u7814\u7a76\u8005\u663e\u793a\u4e86\u8fdc\u79bb\u5206\u5c94\u70b9\u7684\u901f\u7387\u4f9d\u8d56\u7684\u5ef6\u8fdf\u54cd\u5e94\uff0c\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8ddf\u8e2a\u7684\u662f\u4e0d\u7a33\u5b9a\u72b6\u6001\u3002\u7814\u7a76\u8005\u7684\u7814\u7a76\u7ed3\u679c\u5f3a\u8c03\uff0c\u73af\u5883\u53d8\u5316\u7684\u901f\u7387\u53ef\u4ee5\u63ed\u793a\u7cfb\u7edf\u7684\u7a33\u5b9a\u5e73\u8861\u6001\u548c\u5206\u5c94\u70b9\u6240\u4e0d\u80fd\u9884\u6d4b\u7684\u610f\u5916\u706d\u7edd\u52a8\u529b\u5b66\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u8005\u7684\u7ed3\u679c\u8bf4\u660e\u4e86\u5bf9\u4e8e\u7406\u89e3\u4e00\u4e2a\u751f\u6001\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u548c\u6301\u4e45\u6027\u800c\u8a00\uff0c\u901f\u7387\u4f9d\u8d56\u54cd\u5e94\u7684\u91cd\u8981\u6027\u3002<\/span><\/p>\n


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6. \u751f\u6001\u7cfb\u7edf\u4e2d\u7531\u901f\u7387\u5bfc\u81f4\u7684\u7a33\u6001\u8f6c\u53d8<\/strong><\/strong><\/p>\n<\/section>\n

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Extinctions in time-delayed population maps, fallings, and extreme forcing<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

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\u4f17\u6240\u5468\u77e5\uff0c\u5177\u6709\u65f6\u95f4\u5ef6\u8fdf\u7684\u968f\u673a\u79cd\u7fa4\u56fe\u7ecf\u5386\u4e86\u566a\u58f0\u4ecb\u5bfc\u7684\u8f6c\u53d8\uff0c\u5bfc\u81f4\u5176\u7ed3\u6784\u7a33\u5b9a\u6027\u7684\u4e27\u5931\u3002\u7531\u4e8e\u6240\u6d89\u53ca\u7684\u786e\u5b9a\u6027\u548c\u968f\u673a\u65f6\u95f4\u5c3a\u5ea6\u7684\u8026\u5408\uff0c\u8fd9\u79cd\u8fc7\u6e21\u5bf9Ornstein-Uhlenbeck\u5f3a\u8feb\u7684\u566a\u58f0\u76f8\u5173\u65f6\u95f4\u7684\u7279\u5b9a\u503c\u8fdb\u884c\u4e86\u4f18\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u7814\u7a76\u8005\u8bc1\u660e\u4e86\u786e\u5b9a\u6027\u65f6\u95f4\u5c3a\u5ea6\u4e0e\u7cfb\u7edf\u63a5\u8fd1\u7a33\u5b9a\u8fb9\u754c\u7684\u52a8\u529b\u5b66\u6709\u5173\u3002\u8f6c\u4e49\u8fc7\u7a0b\u63cf\u8ff0\u4e86\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u4eba\u7c7b\u68d2\u5e73\u8861<\/span>\uff08human stick balancing\uff09<\/span>\u4e2d\u89c2\u5bdf\u5230\u7684\u751f\u5b58\u5206\u5e03\u51fd\u6570\uff0c\u8be5\u4efb\u52a1\u5df2\u77e5\u6d89\u53ca\u622a\u65ad\u7684 L\u00e9vy \u5f3a\u8feb\u3002<\/span><\/p>\n


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7. \u6e10\u8fd1\u81ea\u6cbb\u7cfb\u7edf\u6df7\u6c8c\u5438\u5f15\u5b50<\/strong><\/strong><\/p>\n

\u7684<\/strong><\/strong>\u7269\u7406\u4e0d\u53d8\u6d4b\u5ea6\u548c\u7a81\u53d8\u6982\u7387<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

Physical invariant measures and tipping probabilities for chaotic attractors of asymptotically autonomous systems<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00114-z<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u7269\u7406\u5ea6\u91cf\u662f\u4e0d\u53d8\u7684\u5ea6\u91cf\uff0c\u7528\u6765\u63cf\u8ff0\u5728\u81ea\u6cbb\u52a8\u529b\u7cfb\u7edf\u7684\u6df7\u6c8c\u5438\u5f15\u5b50\u76c6\u5730\u4e2d\u5f00\u59cb\u7684\u8f68\u8ff9\u7684\u201c\u5178\u578b\u201d\u884c\u4e3a\u3002\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u5c06\u8fd9\u4e00\u6982\u5ff5\u63a8\u5e7f\u5230\u66f4\u4e00\u822c\u7684\u975e\u81ea\u6cbb<\/span>\uff08\u65f6\u53d8\uff09<\/span>\u52a8\u529b\u7cfb\u7edf\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5728\u7269\u7406\u4e0a\u6709\u610f\u4e49\u7684\u65b9\u5f0f\u4e2d\u8fd9\u6837\u505a\u662f\u6709\u969c\u788d\u7684\uff0c\u4f46\u662f\u5bf9\u4e8e\u5177\u6709\u81ea\u4e3b\u9650\u5236\u7684\u7cfb\u7edf\uff0c\u7814\u7a76\u8005\u53ef\u4ee5\u6839\u636e\u8fc7\u53bb\u9650\u5236\u4e2d\u7684\u7269\u7406\u5ea6\u91cf\u6765\u5b9a\u4e49\u7269\u7406\u5ea6\u91cf\u3002\u7814\u7a76\u8005\u5229\u7528\u8fd9\u4e00\u70b9\u6765\u7406\u89e3\u6df7\u6c8c\u5438\u5f15\u5b50\u4e4b\u95f4\u7684\u901f\u7387\u4f9d\u8d56\u7a81\u53d8\u53ef\u4ee5\u7528\u201c\u7a81\u53d8\u6982\u7387\u201d\u6765\u91cf\u5316\u7684\u60c5\u51b5\u3002<\/span><\/p>\n


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\u5728(a)\u4e0d\u53ef\u9006\u901f\u7387\u4f9d\u8d56\u7a81\u53d8a=0.0135\u548c(b)\u77ac\u6001\u901f\u7387\u4f9d\u8d56\u7a81\u53d8a=0.0157\u60c5\u51b5\u4e0b\uff0c\u5177\u6709(17)\u4f4d\u79fb\u7684Stommel-Lorenz\u6a21\u578b(16)\u7684\u901f\u7387\u4f9d\u8d56\u7a81\u53d8:\u5176\u4ed6\u53c2\u6570\u548c\u8be6\u7ec6\u4fe1\u606f\u8bf7\u53c2\u89c1\u6587\u672c\u3002<\/span><\/section>\n


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\u7814\u7a76\u8005\u5728\u4e24\u4e2a\u5177\u6709\u591a\u4e2a\u5438\u5f15\u5b50\u7684\u6444\u52a8\u7cfb\u7edf\u7684\u4f8b\u5b50\u4e2d\u8bc1\u660e\u4e86\u8fd9\u4e00\u70b9\u3002\u7b2c\u4e00\u4e2a\u662fChua\u7b49\u4eba\u7684\u53cc\u6da1\u65cb\u7cfb\u7edf\uff0c\u7b2c\u4e8c\u4e2a\u662fLorenz\u6df7\u6c8c\u5f3a\u8feb\u4e0b\u7684Stommel\u6a21\u578b\u3002<\/span><\/p>\n


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8. \u57fa\u4e8e\u4e3b\u4f53\u6a21\u578b\u7684\u7a81\u53d8\u8def\u5f84\u7edf\u8ba1\u5206\u6790<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

Statistical analysis of tipping pathways in agent-based models<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00191-0<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


<\/p>\n

\u57fa\u4e8e\u4e3b\u4f53<\/span>\uff08agent\uff09<\/span>\u7684\u6a21\u578b\u662f\u6a21\u62df\u590d\u6742\u793e\u4f1a\u7cfb\u7edf\u7684\u81ea\u7136\u9009\u62e9\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u5728\u5fae\u89c2\u5c3a\u5ea6\u4e0a\u7684\u5927\u91cf\u4e2a\u4f53\u7684\u7b80\u5355\u968f\u673a\u76f8\u4e92\u4f5c\u7528\u89c4\u5219\u53ef\u4ee5\u5bfc\u81f4\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u7684\u6d8c\u73b0\u52a8\u529b\u5b66\uff0c\u4f8b\u5982\u591a\u6570\u4eba\u7684\u89c2\u70b9\u6216\u884c\u4e3a\u7684\u7a81\u53d8\u3002<\/span><\/p>\n


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\u4e00\u4e2a\u7531 50 \u4e2a\u4ea4\u4e92\u4e3b\u4f53\u7ec4\u6210\u7684\u5b8c\u6574\u7f51\u7edc\u590d\u6742\u4f20\u67d3\u52a8\u529b\u5b66\u3002a \u5728\u7531\u201c\u5177\u6709\u7eff\u8272\u610f\u89c1\u7684\u4e3b\u4f53\u6570\u91cf\u201d\u548c\u201c\u5177\u6709\u7eff\u8272\u884c\u4e3a\u7684\u4e3b\u4f53\u6570\u91cf\u201d\u4e24\u4e2a\u5750\u6807\u8de8\u8d8a\u7684\u5e73\u9762\u5185\u5177\u6709\u5f88\u5f3a\u7684\u5faa\u73af\u6027\u3002b \u56e0\u6b64\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u901a\u8fc7\u5728\u5750\u6807\u5e73\u9762\u4e2d\u7ed8\u5236\u987a\u65f6\u9488\u89d2\u5ea6\u6765\u53ef\u89c6\u5316\u52a8\u529b\u5b66\uff0c\u5373\u76f8\u4f4d \u03b8t<\/sub>\u3002\u6a21\u578b\u53c2\u6570\u4e3a b,c,f,g=0.7, e=0.02, \u03c4=0.99<\/span><\/section>\n


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\u5728\u672c\u6587\u4e2d\uff0c\u7814\u7a76\u8005\u4ecb\u7ecd\u4e86\u4e00\u79cd\u65b9\u6cd5\u6765\u7814\u7a76\u566a\u58f0\u8bf1\u53d1\u7684\u7a81\u53d8\u4e4b\u95f4\u7684\u76f8\u5173\u5b50\u96c6\u7684\u4e3b\u4f53\u72b6\u6001\u7a7a\u95f4\u8868\u793a\u7279\u5f81\u914d\u7f6e\u3002\u7531\u4e8e\u4e2a\u4f53\u7684\u5927\u91cf\u76f8\u4e92\u4f5c\u7528\uff0c\u57fa\u4e8e\u4e3b\u4f53\u7684\u6a21\u578b\u662f\u9ad8\u7ef4\u7684\uff0c\u4f46\u901a\u5e38\u5b58\u5728\u4e00\u4e2a\u4f4e\u7ef4\u7684\u96c6\u4f53\u884c\u4e3a\u7ed3\u6784\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u8005\u5e94\u7528\u6269\u6563\u56fe\uff0c\u4e00\u79cd\u975e\u7ebf\u6027\u7684\u964d\u7ef4\u6280\u672f\uff0c\u6765\u63ed\u793a\u5185\u5728\u7684\u4f4e\u7ef4\u7ed3\u6784\u3002\u7814\u7a76\u8005\u7528\u8f6c\u79fb\u8def\u5f84\u7406\u8bba\u6765\u63cf\u8ff0\u7a81\u53d8\u884c\u4e3a\uff0c\u8fd9\u6709\u52a9\u4e8e\u7edf\u8ba1\u7406\u89e3\u7a81\u53d8\u8def\u5f84\u7684\u5206\u5e03\u3001\u901a\u91cf\u548c\u901f\u7387\u3002\u901a\u8fc7\u7cfb\u7edf\u5730\u7814\u7a76\u4e24\u79cd\u57fa\u4e8e\u4e3b\u4f53\u7684\u6a21\u578b\uff0c\u5c55\u793a\u4e86\u591a\u79cd\u7a81\u53d8\u9014\u5f84\u548c\u7ea7\u8054\u6548\u5e94\uff0c\u8bf4\u660e\u4e86\u7814\u7a76\u8005\u7684\u65b9\u6cd5\u7684\u5b9e\u7528\u6027\u3002<\/span><\/p>\n


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9. \u901a\u8fc7\u6709\u9488\u5bf9\u6027\u7684\u793e\u4f1a\u758f\u79bb<\/strong><\/strong><\/p>\n

\u79fb\u52a8\u6d41\u884c\u75c5\u7684\u4e34\u754c\u70b9<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

Moving the epidemic tipping point through topologically targeted social distancing<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00138-5<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u4e00\u79cd\u793e\u4f1a\u5236\u5ea6\u7684\u6d41\u884c\u9608\u503c\u662f\u6307\u5f53\u4e00\u79cd\u75be\u75c5\u5728\u8be5\u793e\u4f1a\u5236\u5ea6\u4e2d\u4f20\u64ad\u65f6\uff0c\u5176\u611f\u67d3\u7387\u548c\u6062\u590d\u7387\u8d85\u8fc7\u6d41\u884c\u9608\u503c\u65f6\uff0c\u75be\u75c5\u4fbf\u4f1a\u5728\u8be5\u793e\u4f1a\u4e2d\u8fdb\u884c\u6d41\u884c\u6027\u4f20\u64ad\u3002\u5728\u6ca1\u6709\u836f\u7269\u5e72\u9884\u63aa\u65bd<\/span>\uff08\u5373\u75ab\u82d7\uff09<\/span>\u7684\u60c5\u51b5\u4e0b\uff0c\u63a7\u5236\u7279\u5b9a\u75be\u75c5\u7684\u552f\u4e00\u65b9\u6cd5\u662f\u901a\u8fc7\u793e\u4f1a\u8ddd\u79bb\u7b49\u975e\u836f\u7269\u5e72\u9884\u63aa\u65bd\uff0c\u5c06\u8fd9\u4e00\u9608\u503c\u79fb\u81f3\u4e0e\u8be5\u75be\u75c5\u5bf9\u5e94\u7684\u6d41\u884c\u9608\u503c\u4e4b\u4e0a\uff0c\u4ece\u800c\u4f7f\u7cfb\u7edf\u4ece\u6d41\u884c\u72b6\u6001\u8f6c\u5411\u975e\u6d41\u884c\u72b6\u6001\u3002\u5c06\u75be\u75c5\u5efa\u6a21\u4e3a\u793e\u4ea4\u56fe\u4e0a\u7684\u4f20\u64ad\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u901a\u8fc7\u5220\u9664\u4e00\u4e9b\u56fe\u4e0a\u7684\u94fe\u63a5\u6765\u5efa\u7acb\u793e\u4ea4\u8ddd\u79bb\u6a21\u578b\u3002\u63a8\u6d4b\u7ed3\u679c\u56fe\u90bb\u63a5\u77e9\u9635\u7684\u6700\u5927\u7279\u5f81\u503c\u5bf9\u5e94\u4e8e\u7cfb\u7edf\u6d41\u884c\u9608\u503c\u3002<\/span><\/p>\n


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\u4ece N=100 \u548c E\u2248900 \u7684\u521d\u59cb BA \u548c RG \u56fe\u4e2d\u5220\u9664 80% \u7684\u8054\u7cfb\u4eba\u540e\uff0c\u6765\u81ea\u7f51\u7edc\u96c6\u5408\u7684\u793a\u4f8b\u7f51\u7edc\u3002<\/span><\/section>\n


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\u672c\u6587\u91c7\u7528\u9a6c\u5c14\u53ef\u592b\u94fe\u8499\u7279\u5361\u7f57<\/span>\uff08MCMC\uff09<\/span>\u65b9\u6cd5\u7814\u7a76\u4e86\u90a3\u4e9b\u80fd\u591f\u6709\u6548\u51cf\u5c0f\u90bb\u63a5\u77e9\u9635\u6700\u5927\u7279\u5f81\u503c\u7684\u94fe\u8def\u79fb\u9664\u65b9\u6cd5\u3002MCMC\u65b9\u6cd5\u4ece\u5b9a\u4e49\u4e86\u03bbmax<\/sub>\u671f\u671b\u503c\u7684\u76f8\u5bf9\u6b63\u5219\u7f51\u7edc\u96c6\u6210\u4e2d\u751f\u6210\u6837\u672c\u3002\u6211\u4eec\u5c06\u5176\u79f0\u4e3a\u201c\u826f\u597d\u63a7\u5236\u7f51\u7edc\u96c6\u6210\u201d<\/span>\uff08well- controlled network ensemble, WCNE\uff09<\/span>\uff0c\u5e76\u5c06\u5176\u7ed3\u6784\u4e0e\u76f8\u540c\u94fe\u8def\u5bc6\u5ea6\u7684\u968f\u673a\u51cf\u8584\u7f51\u7edc\u8fdb\u884c\u6bd4\u8f83\u3002\u6211\u4eec\u89c2\u5bdf\u5230\uff0cWCNE\u4e2d\u7684\u7f51\u7edc\u503e\u5411\u4e8e\u5728\u5ea6\u5206\u5e03\u4e0a\u66f4\u52a0\u5747\u5300\uff0c\u5e76\u4f7f\u7528\u8fd9\u79cd\u89c1\u89e3\u5b9a\u4e49\u4e86\u4e24\u79cd\u7279\u522b\u7684\u53bb\u9664\u7b56\u7565\uff0c\u5b83\u4eec\u4e5f\u5927\u5927\u964d\u4f4e\u4e86\u6700\u5927\u7279\u5f81\u503c\u3002\u6709\u9488\u5bf9\u6027\u5730\u5220\u966480%\u7684\u94fe\u63a5\u4e0e\u968f\u673a\u5220\u966490%\u7684\u94fe\u63a5\u4e00\u6837\u6709\u6548\uff0c\u8fd9\u4f7f\u5f97\u4e2a\u4f53\u7684\u8054\u7cfb\u4eba\u6570\u91cf\u589e\u52a0\u4e86\u4e00\u500d\u3002\u6700\u540e\uff0c\u901a\u8fc7SIS\u6216SIR\u6a21\u578b\u6a21\u62df\u4f20\u67d3\u75c5\u7684\u4f20\u64ad\uff0c\u4ee5\u4e0d\u540c\u7684\u94fe\u8def\u79fb\u9664\u7b56\u7565<\/span>\uff08\u968f\u673a\u3001WCNE\u6216\u5ea6\u5747\u5316\uff09<\/span>\u521b\u5efa\u7684\u7f51\u7edc\u96c6\u6210\uff0c\u6211\u4eec\u53d1\u73b0\uff0cWCNE\u548c\u5ea6\u5747\u5316\u7f51\u7edc\u7684\u4f20\u67d3\u7387\u548c\u6062\u590d\u7387\u7684\u4e34\u754c\u6bd4\u6bd4\u968f\u673a\u53bb\u9664\u5f97\u5230\u7684\u7f51\u7edc\u7684\u4f20\u67d3\u7387\u548c\u6062\u590d\u7387\u7684\u4e34\u754c\u6bd4\u66f4\u5927\u3002<\/span><\/p>\n


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10. \u6291\u5236\u566a\u58f0\u5f15\u8d77\u7684\u4e34\u754c\u8fc7\u6e21\uff1a<\/strong><\/strong><\/p>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

Suppression of noise-induced critical transitions: a linear augmentation method<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00112-1<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5728\u968f\u673a\u590d\u6742\u7cfb\u7edf\u4e2d\uff0c\u7531\u4e8e\u566a\u58f0\u7684\u5b58\u5728\uff0c\u4ece\u4e00\u79cd\u7406\u60f3\u72b6\u6001\u5230\u53e6\u4e00\u79cd\u76f8\u53cd\u72b6\u6001\u7684\u7a81\u7136\u4e34\u754c\u8fc7\u6e21<\/span>\uff08ct\uff09<\/span>\u53ef\u80fd\u4f1a\u53d1\u751f\uff0c\u8fd9\u751a\u81f3\u53ef\u80fd\u5bfc\u81f4\u707e\u96be\u6027\u7684\u540e\u679c\u3002\u4e3a\u4e86\u4f7f\u67d0\u4e2a\u7cfb\u7edf\u4fdd\u6301\u4e00\u79cd\u7406\u60f3\u7684\u6027\u80fd\u72b6\u6001\uff0c\u9700\u8981\u5f00\u53d1\u5728\u566a\u58f0\u5b58\u5728\u65f6\u6291\u5236\u8fd9\u4e9b\u707e\u96be\u6027ct\u7684\u65b9\u6cd5\u3002<\/span><\/p>\n


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11. \u877e\u8788\u95ea\u70c1\u89c6\u89c9\u540c\u6b65\u500d\u5468\u671f\u4e34\u754c\u51cf\u901f\u6307\u6807<\/strong><\/strong><\/p>\n<\/section>\n

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Critical slowing down indicators in synchronous period-doubling for salamander flicker vision<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00113-0<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u8bb8\u591a\u52a8\u529b\u7cfb\u7edf\uff0c\u7279\u522b\u662f\u751f\u7269\u52a8\u529b\u7cfb\u7edf\uff0c\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u72b6\u6001\uff0c\u5728\u8fd9\u4e9b\u72b6\u6001\u4e2d\uff0c\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u901a\u8fc7\u4e00\u4e2a\u4e34\u754c\u8fc7\u6e21\u4ece\u4e00\u4e2a\u72b6\u6001\u53d8\u5316\u5230\u53e6\u4e00\u4e2a\u72b6\u6001\u3002\u8fd9\u4e9b\u8f6c\u53d8\u662f\u4e34\u754c\u70b9<\/span>\uff08CPs\uff09<\/span>\u3002\u5f53\u5438\u5f15\u5b50\u53d8\u5f97\u8106\u5f31\u65f6\uff0cCPs\u53ef\u4ee5\u89c2\u5bdf\u5230\u4e34\u754c\u6162\u5316\u73b0\u8c61\u3002\u7531\u4e8eCPs\u7684\u91cd\u8981\u6027\uff0c\u4e0d\u540c\u7684\u6307\u6807\uff0c\u5982\u65b9\u5dee\uff0c\u81ea\u76f8\u5173\uff0c\u5cf0\u5ea6\uff0c\u504f\u6001\uff0c\u591a\u5e74\u6765\u4e00\u76f4\u662f\u672c\u5b66\u79d1\u4e2d\u7684\u7814\u7a76\u70ed\u70b9\u3002<\/span><\/p>\n


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\u4ee5\u5bf9\u6bd4\u5ea6\u4e3a\u63a7\u5236\u53c2\u6570\u7684\u877e\u8788 ERG a \u7684\u5206\u5c94\u56fe\uff08\u95ea\u5149\u9891\u7387 = 16 Hz\uff09\uff1b\u5c06\u95ea\u5149\u9891\u7387\u89c6\u4e3a\u63a7\u5236\u53c2\u6570\uff08\u5bf9\u6bd4\u5ea6 = 1.0\uff09<\/span><\/section>\n


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\u672c\u6587\u4ece\u877e\u8788\u7684\u773c\u775b\u4e2d\u8bb0\u5f55\u4e86\u89c6\u7f51\u819c\u7535\u56fe<\/span>\uff08ERGs\uff09<\/span>\uff0c\u7814\u7a76\u4e86\u56db\u4e2a\u516c\u8ba4\u7684CP\u6307\u6807\u3002\u4e3a\u4e86\u7814\u7a76\u8fd9\u4e9b\u8457\u540d\u7684\u6307\u6807\u9884\u6d4b\u877e\u8788ERGs\u5206\u5c94\u7cfb\u7edf\u52a8\u529b\u5b66\u53d8\u5316\u7684\u80fd\u529b\uff0c\u9996\u5148\uff0c\u4f7f\u7528\u4eba\u5de5\u9608\u503c\u68c0\u6d4b\u7cfb\u7edf\u7684\u4e0d\u540c\u52a8\u529b\u5b66\u3002\u7136\u540e\u5229\u7528\u8fd9\u56db\u4e2a\u6307\u6807\u5b9e\u73b0\u9884\u8b66\u4fe1\u53f7\u3002\u7ed3\u679c\u8868\u660e\u65b9\u5dee\u6307\u6807\u6709\u5e0c\u671b\u4f5c\u4e3a\u4e00\u4e2a\u503c\u5f97\u4fe1\u8d56\u7684\u6307\u6807\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u4e00\u4e2a\u9884\u8b66\u4fe1\u53f7\u3002\u6b64\u5916\uff0c\u5cf0\u5ea6\u548c\u504f\u5ea6\u662f\u6700\u4e0d\u7406\u60f3\u7684\u6307\u6807\uff0c\u56e0\u4e3a\u5b83\u4eec\u5bf9\u566a\u58f0\u975e\u5e38\u654f\u611f\uff0c\u800c\u566a\u58f0\u662f\u771f\u5b9e\u6570\u636e\u7684\u56fa\u6709\u5c5e\u6027\u3002\u867d\u7136\u50cf\u65b9\u5dee\u4e00\u6837\uff0c\u81ea\u76f8\u5173\u53ef\u4ee5\u5f97\u5230\u51c6\u786e\u7684\u7ed3\u679c\uff0c\u4f46\u5b83\u5305\u542b\u4e86\u8bb8\u591a\u5047\u9633\u6027\uff0c\u4ece\u800c\u964d\u4f4e\u4e86\u8be5\u6307\u6807\u4f5c\u4e3aCPs\u65e9\u671f\u9884\u8b66\u4fe1\u53f7\u7684\u53ef\u9760\u6027\u3002\u5e76\u4e14\u6307\u51fa\uff0c\u5728\u6bcf\u4e2a\u5206\u5c94\u53c2\u6570\u4e2d\u9002\u5f53\u7684\u6570\u636e\u957f\u5ea6\u53ef\u4ee5\u5f97\u5230\u66f4\u53ef\u9760\u7684\u9884\u8b66\u4fe1\u53f7\u3002<\/span><\/p>\n


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12. \u4e24\u5c42\u7f51\u7edc\u4e0a\u591a\u8def\u590d\u7528\u5f15\u8d77\u7684\u7a81\u53d8<\/strong><\/strong><\/p>\n<\/section>\n

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Tipping induced by multiplexing on two-layer networks 
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https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00116-x<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u7814\u7a76\u8005\u62a5\u544a\u4e86\u7531\u4e8e\u4e0e\u53e6\u4e00\u4e2a\u7cfb\u7edf\u7f51\u7edc\u7684\u591a\u8def\u590d\u7528\u800c\u5728\u7cfb\u7edf\u4e2d\u8bf1\u5bfc\u7684\u7a81\u7136\u8fc7\u6e21\u6216\u7a81\u53d8\u7684\u7814\u7a76\u3002\u7531\u4e8e\u4e0e\u5171\u4eab\u73af\u5883\u7684\u95f4\u63a5\u8026\u5408\u3001\u5e73\u5747\u573a\u8026\u5408\u548c\u5b83\u4eec\u4e4b\u95f4\u7684\u5171\u8f6d\u8026\u5408\uff0c\u4e00\u5c42\u632f\u8361\u7684\u7a81\u53d1\u52a8\u529b\u5b66\u4f1a\u53d1\u751f\u7a81\u7136\u5411\u7a33\u6001\u7684\u8f6c\u53d8\u3002\u5728\u6240\u6709\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u5f53\u4e0e\u53e6\u4e00\u7ec4\u7c7b\u4f3c\u7684\u7cfb\u7edf\u590d\u7528\u65f6\uff0c\u5728\u7b2c\u4e8c\u5c42\u8bf1\u53d1\u7684\u7a81\u53d8\u73b0\u8c61\u4e5f\u5177\u6709\u7c7b\u4f3c\u7684\u884c\u4e3a\u6a21\u5f0f\u3002<\/span><\/p>\n


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\u8026\u5408\u8303\u5fb7\u6ce2\u5c14\u632f\u8361\u5668\u7684\u591a\u91cd\u7f51\u7edc\u4e2d\u4ece\u632f\u8361\u72b6\u6001\u5230\u6b7b\u4ea1\u72b6\u6001\u7684\u8f6c\u53d8\u3002L1 \u5c42\uff08\u5de6\u56fe\uff09\u5177\u6709 S-F \u8026\u5408\u62d3\u6251\uff0c\u4ee5\u53ca\u5171\u4eab\u73af\u5883\uff0cL2 \u5c42\uff08\u53f3\u56fe\uff09\u5f62\u6210\u4e00\u7ec4\u975e\u8026\u5408\u7cfb\u7edf\uff0c\u6bcf\u4e2a\u7cfb\u7edf\u4e2d\u6709 N \u4e2a\u632f\u8361\u5668\u3002a1, b1 \u9636\u53c2\u6570\uff0cA(\u03bb1<\/sub>)\uff0c\u5728\u8026\u5408\u5f3a\u5ea6 \u03bb1<\/sub> \u7edd\u70ed\u53d8\u5316\u4e0b\uff0c\u5411\u524d\uff08\u7ea2\u8272\uff09\u548c\u5411\u540e\uff08\u7eff\u8272\uff09\u65b9\u5411\uff0c<k1>=6\uff1ba2, b2 \u5904\u4e8e\u6b7b\u4ea1\u72b6\u6001\u7684\u632f\u8361\u5668\u4e0e\u603b\u6570\u7684\u6bd4\u503c\uff0cNd<\/sub>\/N\uff0c\u5411\u524d\u8fde\u7eed\u7ed8\u5236\uff0c<k1>=6\uff1ba3, b3 \u8fc7\u6e21\u671f\u95f4\u7684\u9636\u53c2\u6570\uff0c<k1>=20 \u548c a4,b4 Nd<\/sub>\/N\uff0c<k1>=20\u3002\u5176\u4ed6\u53c2\u6570\u4e3a b=1\u3001\u03b5=1.5\u3001\u03b7=1\u3001\u03bb2<\/sub>=0.0 \u548c N=500\u3002\u5373\u4f7f L2 \u7684\u632f\u8361\u5668\u4e0d\u8026\u5408\uff0cL1 \u4e0a\u53d1\u751f\u7684\u503e\u7ffb\u4e5f\u4f1a\u5728 L2 \u4e0a\u5f15\u8d77\u7c7b\u4f3c\u7684\u8f6c\u53d8\u6a21\u5f0f\u3002\u4e34\u754c\u70b9\u968f\u7740 <k1> \u7684\u53d8\u5316\u800c\u6539\u53d8<\/span><\/section>\n


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13. \u54e5\u672c\u54c8\u6839\u7f51\u7edc\u7814\u7a76\u4e2d<\/strong><\/strong><\/p>\n

\u63a2\u7d22\u793e\u4f1a\u4f20\u67d3\u7684\u5242\u91cf-\u53cd\u5e94\u51fd\u6570\u548c\u66ff\u4ee3\u6a21\u578b<\/strong><\/strong><\/p>\n<\/section>\n

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Dose\u2013response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

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\u7f51\u7edc\u4f20\u64ad\u52a8\u529b\u5b66\u548c\u590d\u6742\u4f20\u67d3\u8fc7\u7a0b\u662f\u590d\u6742\u7684\u4eba\u4e0e\u81ea\u7136\u7cfb\u7edf\u4e2d\u5173\u952e\u8fc7\u6e21\u3001\u7a81\u53d8\u70b9\u7b49\u975e\u7ebf\u6027\u73b0\u8c61\u51fa\u73b0\u7684\u91cd\u8981\u673a\u5236\u3002\u73b0\u5728\u8d8a\u6765\u8d8a\u591a\u7684\u65f6\u95f4\u7f51\u7edc\u6570\u636e\u53ef\u7528\u6765\u7814\u7a76\u8fd9\u79cd\u884c\u4e3a\u3001\u89c2\u70b9\u3001\u601d\u60f3\u3001\u75be\u75c5\u548c\u521b\u65b0\u7684\u4f20\u64ad\u8fc7\u7a0b\uff0c\u4ee5\u68c0\u9a8c\u5173\u4e8e\u5176\u7279\u5b9a\u5c5e\u6027\u7684\u5047\u8bbe\u3002<\/span><\/p>\n


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\u54e5\u672c\u54c8\u6839\u7f51\u7edc\u7814\u7a76\uff1a\u7b2c\u4e00\u5b66\u671f\u5178\u578b\u4e00\u5929\u7684\u65f6\u95f4\u7f51\u7edc\u5feb\u7167\u3002\u6bcf\u4e2a\u70b9\u4ee3\u8868\u4e00\u4e2a\u4e2a\u4f53\uff0c\u6839\u636e\u4ece\u5355\u4e2a\u8282\u70b9\uff08\u6df1\u84dd\u8272\uff09\u5230\u5927\u578b\u96c6\u7fa4\uff08\u6df1\u7ea2\u8272\uff09\u7684\u96c6\u7fa4\u5927\u5c0f\u8fdb\u884c\u989c\u8272\u7f16\u7801\u3002\u5feb\u7167\u4e2d\u660e\u663e\u7684\u8282\u70b9\u7c07\u5bf9\u5e94\u4e8e\u53c2\u4e0e\u6d3b\u52a8\u7684\u5b66\u751f\uff0c\u4f8b\u5982\u8bb2\u5ea7\u6216\u5728\u81ea\u52a9\u9910\u5385\u5403\u5348\u9910<\/span><\/section>\n


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\u4e3a\u6b64\uff0c\u7814\u7a76\u8005\u5728\u8fd9\u91cc\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u5242\u91cf\u53cd\u5e94\u51fd\u6570\u548c\u4f7f\u7528\u66ff\u4ee3\u6570\u636e\u6a21\u578b\u7684\u5047\u8bbe\u68c0\u9a8c\u7684\u65b9\u6cd5\uff0c\u8be5\u6a21\u578b\u968f\u673a\u5316\u4e86\u7ecf\u9a8c\u6570\u636e\u7684\u5927\u90e8\u5206\u65b9\u9762\uff0c\u540c\u65f6\u4fdd\u7559\u4e86\u4e0e\u4f20\u67d3\u3001\u7fa4\u4f53\u6216\u540c\u8d28\u6027\u52a8\u529b\u5b66\u76f8\u5173\u7684\u67d0\u4e9b\u7ed3\u6784\u3002\u7814\u7a76\u8005\u8bc1\u660e\u4e86\u8fd9\u79cd\u65b9\u6cd5\u7684\u5408\u6210\u65f6\u95f4\u7f51\u7edc\u6570\u636e\u7684\u6269\u5c55\u8fc7\u7a0b\u4ea7\u751f\u7684\u81ea\u9002\u5e94\u6295\u7968\u4eba\u6a21\u578b\u3002\u6b64\u5916\uff0c\u7814\u7a76\u8005\u5c06\u5176\u5e94\u7528\u4e8e\u54e5\u672c\u54c8\u6839\u7f51\u7edc\u7814\u7a76\u7684\u7ecf\u9a8c\u65f6\u95f4\u7f51\u7edc\u6570\u636e\u3002\u8fd9\u4e2a\u6570\u636e\u96c6\u63d0\u4f9b\u4e86\u6570\u767e\u540d\u53c2\u4e0e\u7814\u7a76\u7684\u5927\u5b66\u751f\u5728\u4e09\u4e2a\u6708\u7684\u65f6\u95f4\u91cc\u8eab\u4f53\u4e0a\u7684\u7d27\u5bc6\u8054\u7cfb\u7f51\u7edc\u3002\u7814\u7a76\u8005\u5728\u8fd9\u4e2a\u7f51\u7edc\u4e0a\u7814\u7a76\u4e0e\u5065\u5eb7\u6709\u5173\u7684\u201c\u5b9a\u671f\u53bb\u5065\u8eab\u623f\u201d\u884c\u4e3a\u7684\u6f5c\u5728\u4f20\u64ad\u52a8\u529b\u5b66\u3002\u57fa\u4e8e\u4e3b\u4f53\u6570\u636e\u6a21\u578b\u7684\u5c42\u6b21\u7ed3\u6784\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u7814\u7a76\u8005\u7684\u65b9\u6cd5\u65e2\u6ca1\u6709\u4e3a\u8be5\u6570\u636e\u96c6\u4e2d\u5242\u91cf-\u53cd\u5e94\u578b\u7f51\u7edc\u4f20\u64ad\u8fc7\u7a0b\u7684\u5f71\u54cd\u63d0\u4f9b\u663e\u8457\u8bc1\u636e\uff0c\u4e5f\u6ca1\u6709\u4e3a\u540c\u8d28\u6027\u63d0\u4f9b\u663e\u8457\u8bc1\u636e\u3002\u8fd0\u52a8\u884c\u4e3a\u7684\u7ecf\u9a8c\u52a8\u529b\u5b66\u53ef\u80fd\u66f4\u597d\u5730\u7531\u4e2a\u4f53\u7279\u5f81\u6765\u63cf\u8ff0\uff0c\u5982\u5bf9\u884c\u4e3a\u7684\u503e\u5411\u3001\u7ef4\u6301\u884c\u4e3a\u7684\u6301\u4e45\u6027\u3001\u5f71\u54cd\u6574\u4e2a\u7fa4\u4f53\u7684\u5916\u90e8\u5f71\u54cd\u4ee5\u53ca\u975e\u5e73\u51e1\u7f51\u7edc\u7ed3\u6784\u3002\u8be5\u65b9\u6cd5\u5177\u6709\u901a\u7528\u6027\uff0c\u4e5f\u53ef\u5e94\u7528\u4e8e\u5176\u4ed6\u65f6\u95f4\u7f51\u7edc\u6570\u636e\u96c6\u548c\u611f\u5174\u8da3\u7684\u7279\u5f81\u3002<\/span><\/p>\n


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14. \u5806\u80a5\u70b8\u5f39\u5728\u8fde\u7eed\u6781\u9650\u4e2d\u7684\u4e0d\u7a33\u5b9a\u6027<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/h3>\n

The compost bomb instability in the continuum limit<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00013-3<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u201c\u5806\u80a5\u70b8\u5f39\u201d\u7684\u4e0d\u7a33\u5b9a\u6027\u662f\u6307\u571f\u58e4\u6e29\u5ea6\u4e0d\u53d7\u63a7\u5236\u7684\u5347\u9ad8\u3002\u5f53\u8db3\u591f\u5feb\u7684\u53d8\u6696\u589e\u52a0\u571f\u58e4\u5f02\u517b\u547c\u5438\u4f5c\u7528\u65f6\uff0c\u5c31\u4f1a\u5f15\u8d77\u8fd9\u79cd\u4e0d\u7a33\u5b9a\u6027\uff0c\u800c\u5f02\u517b\u547c\u5438\u4f5c\u7528\u53c8\u4f1a\u8fdb\u4e00\u6b65\u52a0\u70ed\u571f\u58e4\u3002\u8fd9\u4f1a\u4ea7\u751f\u5931\u63a7\u6548\u5e94\uff0c\u4f7f\u571f\u58e4\u6e29\u5ea6\u8fc5\u901f\u5347\u9ad8\u3002\u672c\u6587\u7814\u7a76\u4e86\u8fd9\u4e2a\u5728\u5730\u7403\u7cfb\u7edf\u6a21\u578b\u4e2d\u88ab\u5ffd\u7565\u7684\u8fc7\u7a0b\uff0c\u8fc4\u4eca\u4e3a\u6b62\uff0c\u5b83\u5df2\u88ab\u901a\u8fc7\u4f7f\u7528\u5e38\u5fae\u5206\u65b9\u7a0b\u7684\u6982\u5ff5\u6a21\u578b\u8fdb\u884c\u4e86\u5206\u6790\u3002\u4f46\u8be5\u6a21\u578b\u88ab\u8fc7\u5ea6\u7406\u60f3\u5316\uff0c\u6a21\u578b\u4e2d\u4e0d\u5b58\u5728\u4efb\u4f55\u571f\u58e4\u7a7a\u95f4\u7ed3\u6784\u7684\u8868\u793a\u3002<\/span><\/p>\n


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\u571f\u58e4\u6e29\u5ea6 Ts<\/sub>(z,t) \u7684\u70ed\u6269\u6563\u65b9\u7a0b<\/span><\/p>\n


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\u5728\u6b64\uff0c\u7814\u7a76\u8005\u4f7f\u7528\u504f\u5fae\u5206\u65b9\u7a0b\uff0c\u5728\u8003\u8651\u571f\u58e4\u6df1\u5ea6\u65f6\u4ecd\u7136\u4f1a\u51fa\u73b0\u8fd9\u79cd\u5931\u63a7\u6548\u5e94\u3002\u4f7f\u7528\u8fd9\u79cd\u8f83\u65b0\u7684\u6a21\u578b\uff0c\u672c\u6587\u7814\u7a76\u4e86\u4f7f\u571f\u58e4\u5bb9\u6613\u53d7\u5230\u8fd9\u79cd\u4e0d\u7a33\u5b9a\u6027\u5f71\u54cd\u7684\u5f3a\u8feb\u53c2\u6570\u3002\u7279\u522b\u662f\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u5371\u9669\u7684\u5927\u5b63\u8282\u5faa\u73af\u53d8\u5316\u5bf9\u6c14\u6e29\u7684\u5f71\u54cd\u53ef\u4ee5\u4e3a\u201c\u5806\u80a5\u70b8\u5f39\u201d\u70ed\u4e0d\u7a33\u5b9a\u6027\u521b\u9020\u5408\u7406\u7684\u6761\u4ef6\u3002<\/span><\/p>\n


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15. \u57fa\u4e8e\u536b\u661f\u548c\u89c2\u6d4b\u6570\u636e\u7684<\/strong><\/strong><\/p>\n

\u76c6\u5730\u964d\u6c34\u7f51\u7edc\u63a2\u6d4b<\/strong><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

Network-based exploration of basin precipitation based on satellite and observed data<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00017-z<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5145\u8db3\u548c\u6709\u6548\u7684\u964d\u6c34\u6570\u636e\u7531\u4e8e\u5176\u65f6\u7a7a\u53d8\u5f02\u6027\u4ee5\u53ca\u5730\u5f62\u548c\u6c14\u5019\u56e0\u7d20\u662f\u4e00\u4e2a\u4e3b\u8981\u95ee\u9898\u3002\u57fa\u4e8e\u536b\u661f\u7684\u4ea7\u54c1\u662f\u5bf9\u5730\u5f62\u590d\u6742\u548c\u6c14\u5019\u591a\u6837\u7684\u76c6\u5730\u8fdb\u884c\u53ef\u9760\u964d\u6c34\u4f30\u8ba1\u7684\u53e6\u4e00\u79cd\u9009\u62e9\u3002\u514d\u8d39\u63d0\u4f9b\u8986\u76d6\u5168\u7403\u548c\u8fde\u7eed\u6570\u636e\u7684\u536b\u661f\u4ea7\u54c1;\u7136\u800c\uff0c\u7406\u89e3\u7a7a\u95f4\u8054\u7cfb\u5bf9\u4e8e\u53ef\u9760\u7684\u6c34\u6587\u5e94\u7528\u81f3\u5173\u91cd\u8981\u3002<\/span><\/p>\n


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P-Network\uff08\u9762\u677f I\uff09\u548c S-Network\uff08\u9762\u677f II\uff09\u7684\u4e0d\u540c\u76f8\u5173\u9608\u503c\u7684\u805a\u7c7b\u7cfb\u6570\u503c\u3002\u5728\u4e24\u4e2a\u9762\u677f\u4e2d\uff0c\uff08a-d\uff09\u4ee3\u8868 TRMM \u7f51\u7edc\uff0c\uff08e-h\uff09\u4ee3\u8868IMD \u7f51\u7edc<\/span><\/section>\n


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\u672c\u7814\u7a76\u91c7\u7528\u805a\u7c7b\u7cfb\u6570\u3001\u5ea6\u5206\u5e03\u3001\u5e73\u5747\u90bb\u57df\u548c\u5efa\u7b51\u7b49\u590d\u6742\u7f51\u7edc\u6982\u5ff5\u6765\u7814\u7a76\u76c6\u5730\u7684\u7a7a\u95f4\u8fde\u63a5\u3002\u7814\u7a76\u8005\u8fd8\u5229\u7528\u52a0\u6743\u95f4\u5ea6\u786e\u5b9a\u4e86\u964d\u6c34\u7f51\u7edc\u4e2d\u6709\u5f71\u54cd\u7684\u683c\u70b9\u3002\u7ed3\u679c\u8868\u660e\uff0c\u76f8\u5173\u6027\u65b9\u6cd5\u5bf9\u7f51\u7edc\u62d3\u6251\u7ed3\u6784\u6ca1\u6709\u663e\u8457\u5f71\u54cd\u3002\u4f46\u76f8\u5173\u9608\u503c\u5f71\u54cd\u964d\u6c34\u7f51\u7edc\u7684\u805a\u7c7b\u7cfb\u6570\u548c\u5ea6\u503c\u7684\u7a7a\u95f4\u5206\u5e03\u3002\u805a\u7c7b\u7cfb\u6570\u548c\u805a\u7c7b\u5ea6\u7684\u7a7a\u95f4\u5206\u5e03\u4e0e\u76f8\u4f3c\u6027\u6d4b\u5ea6\u548c\u76f8\u5173\u9608\u503c\u65e0\u5173\uff0c\u5448\u53cd\u6bd4\u5173\u7cfb\u3002\u57fa\u4e8e\u536b\u661f\u548c\u89c2\u6d4b\u6570\u636e\u7684\u964d\u6c34\u4f53\u7cfb\u7ed3\u6784\u5728\u4e00\u5b9a\u7684\u76f8\u5173\u9608\u503c\u8303\u56f4\u5185\u8868\u73b0\u51fa\u5c0f\u4e16\u754c\u884c\u4e3a\u3002\u7814\u7a76\u8005\u7684\u53d1\u73b0\u63ed\u793a\u4e86\u7a7a\u95f4\u964d\u6c34\u8054\u7cfb\uff0c\u5e76\u4e3a\u8fdb\u4e00\u6b65\u7684\u6c34\u6587\u5e94\u7528\u7814\u7a76\u63d0\u4f9b\u4e86\u9014\u5f84\u3002<\/span><\/p>\n


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16. \u7528\u53cc\u6d41\u4f53\u91cf\u5b50\u6d41\u4f53\u529b\u5b66\u6a21\u578b<\/strong><\/strong><\/p>\n

\u7814\u7a76<\/strong><\/strong>\u78c1\u5316\u91cf\u5b50\u7b49\u79bb\u5b50\u4f53\u4e2d\u5c18\u57c3\u58f0\u6ce2\u7684<\/strong><\/strong><\/p>\n

\u591a\u7ef4\u4e0d\u7a33\u5b9a\u6027<\/strong><\/strong><\/p>\n<\/section>\n

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Multi-dimensional instability of dust acoustic waves in magnetized quantum plasmas by two-fluid quantum hydrodynamics model<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00110-3<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u672c\u6587\u7814\u7a76\u4e86\u7531\u5e26\u8d1f\u7535\u8377\u548c\u6b63\u7535\u8377\u7684\u53ef\u79fb\u52a8\u5c18\u57c3\u3001\u65e0\u95f4\u9699\u91cf\u5b50\u7535\u5b50\u548c\u79bb\u5b50\u7ec4\u6210\u7684\u78c1\u5316\u5c18\u57c3\u7b49\u79bb\u5b50\u4f53\u4e2d\u5c18\u57c3\u58f0\u6ce2<\/span>\uff08daw\uff09<\/span>\u7684\u53cc\u6d41\u4f53\u91cf\u5b50\u6d41\u4f53\u52a8\u529b\u5b66\u6a21\u578b<\/span>\uff08QHM\uff09<\/span>\u3002\u5229\u7528\u7ea6\u5316\u6444\u52a8\u6280\u672f\u5bfc\u51fa\u4e86Zakharov-Kuznetsov<\/span>\uff08ZK\uff09<\/span>\u65b9\u7a0b\uff0c\u672c\u6587\u7ed9\u51fa\u4e86ZK\u65b9\u7a0b\u7684\u5b64\u7acb\u6ce2\u89e3\uff0c\u5e76\u5bf9\u7c89\u5c18\u6676\u4f53\u4e2d\u7684\u53c2\u6570\u89e3\u8fdb\u884c\u4e86\u6570\u503c\u5206\u6790\uff0c\u7814\u7a76\u4e86\u6b63\u3001\u8d1f\u7c89\u5c18\u6761\u4ef6\u4e0b\u7684daw\u7684\u6027\u8d28\u3002<\/span><\/p>\n


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ZK\u65b9\u7a0b\u7684\u5f62\u5f0f<\/span><\/p>\n


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\u540c\u65f6\uff0c\u672c\u6587\u7528\u5c0fk\u6444\u52a8\u65b9\u6cd5\u7814\u7a76\u4e86\u8fd9\u4e9b\u5b64\u7acb\u6ce2\u7684\u591a\u7ef4\u4e0d\u7a33\u5b9a\u6027\u3002\u4e0d\u7a33\u5b9a\u6027\u5224\u636e\u548c\u4f9d\u8d56\u4e8e\u503e\u89d2\u7684\u751f\u957f\u901f\u7387\u3001\u79bb\u5b50\u4e0e\u5c18\u57c3\u7684\u5bc6\u5ea6\u6bd4\u3001\u5c18\u57c3\u7684\u56de\u65cb\u9891\u7387\u4ee5\u53ca\u7535\u5b50\u4e0e\u79bb\u5b50\u7684\u8d39\u7c73\u6e29\u5ea6\u6bd4\uff0c\u8ba8\u8bba\u4e86\u538b\u7f29\u5b64\u7acb\u6ce2<\/span>\uff08CSWs\uff09<\/span>\u548c\u7a00\u758f\u5b64\u7acb\u6ce2<\/span>\uff08RSWs\uff09<\/span>\u7684\u91cf\u5b50\u884d\u5c04\u53c2\u6570\u4ee5\u53ca\u6b63\u5c18\u57c3\u548c\u8d1f\u5c18\u57c3\u7684\u7535\u8377\u8d28\u91cf\u6bd4\u3002\u8fd9\u4e9b\u7ed3\u679c\u5bf9\u767d\u77ee\u661f\u548c\u78c1\u661f\u5185\u90e8\u7684\u610f\u4e49\u5df2\u4f5c\u4e86\u7b80\u8981\u7684\u8ba8\u8bba\u3002<\/span><\/p>\n


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17. \u566a\u58f0\u5bf9\u78c1\u611f\u5e94\u53ef\u6fc0\u4ecb\u8d28\u4e2d\u6ce2\u4f20\u64ad\u7684\u5f71\u54cd<\/strong><\/strong><\/p>\n<\/section>\n

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Effects of noise on the wave propagation in an excitable media with magnetic induction<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00115-y<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u672c\u6587\u7814\u7a76\u4e86\u8003\u8651\u78c1\u611f\u5e94\u7684\u6539\u8fdb\u7684hindmarshs – rose\u795e\u7ecf\u5143\u6a21\u578b\u7684\u6ce2\u4f20\u64ad\u73b0\u8c61\u548c\u7f51\u7edc\u52a8\u529b\u5b66\u3002\u5229\u7528\u7279\u5f81\u503c\u3001\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u548c\u5206\u652f\u56fe\u8ba8\u8bba\u4e86\u6539\u8fdb\u795e\u7ecf\u5143\u6a21\u578b\u7684\u52a8\u529b\u5b66\u6027\u8d28\u3002\u5bf9\u6307\u6570\u578b\u548c\u4e8c\u6b21\u578b\u78c1\u94fe\u6a21\u578b\u8fdb\u884c\u4e86\u7b80\u5355\u7684\u6bd4\u8f83\uff0c\u7ed3\u679c\u8868\u660e\uff0c\u6307\u6570\u578b\u78c1\u94fe\u6a21\u578b\u53ef\u4ee5\u8868\u73b0\u51fa\u4e0e\u4e8c\u6b21\u578b\u6a21\u578b\u76f8\u4f3c\u7684\u7279\u6027\uff0c\u5373\u78c1\u94fe\u7535\u963b\u968f\u7535\u538b\u6781\u6027\u7684\u53d8\u5316\u5448\u5355\u8c03\u9012\u589e\u6216\u9012\u51cf\u7684\u8d8b\u52bf\u3002<\/span><\/p>\n


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\u5177\u6709\u6307\u6570\u901a\u91cf\u8026\u5408\u7684\u5916\u90e8\u7535\u78c1\u8f90\u5c04\u7684\u65e0\u91cf\u7eb2\u5f62\u5f0f<\/span><\/p>\n


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\u5728\u7f51\u7edc\u52a8\u529b\u5b66\u7814\u7a76\u4e2d\uff0c\u7814\u7a76\u8005\u8003\u8651\u4e86\u4e24\u4e2a\u989d\u5916\u7684\u5916\u90e8\u5e72\u6270\uff0c\u5982\u566a\u58f0\u548c\u901a\u91cf\u6fc0\u52b1\u3002\u5b9a\u4e49\u4e86\u5177\u6709Box-Mueller\u578b\u968f\u673a\u566a\u58f0\u548c\u6b63\u5f26\u5468\u671f\u78c1\u94fe\u6fc0\u52b1\u7684\u6676\u683c\u9635\u7684\u6570\u5b66\u6a21\u578b\u3002\u4ee5\u566a\u58f0\u65b9\u5dee\u4f5c\u4e3a\u63a7\u5236\u53c2\u6570\uff0c\u7814\u7a76\u4e86\u566a\u58f0\u5b58\u5728\u65f6\u7684\u6ce2\u4f20\u64ad\u73b0\u8c61\u3002\u7814\u7a76\u8005\u53ef\u4ee5\u8bc1\u660e\uff0c\u5f53\u566a\u58f0\u5e94\u7528\u5230\u7f51\u7edc\u6574\u4e2a\u6a21\u62df\u65f6\u95f4\uff0c\u87ba\u65cb\u6ce2\u662f\u6709\u6548\u5730\u6291\u5236\u975e\u5e38\u4f4e\u7684\u566a\u58f0\u65b9\u5dee\u503c\u3002<\/span><\/p>\n


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18. \u5728\u6bd4\u4f8b\u4f9d\u8d56\u7684\u7fa4\u843d\u52a8\u529b\u5b66\u6a21\u578b\u4e2d<\/strong><\/strong><\/p>\n

\u52a0\u5165\u5916\u90e8\u566a\u58f0\uff0c<\/strong><\/strong>\u53ea\u6709\u6a21\u62df\u7269\u79cd\u624d\u80fd\u751f\u5b58<\/strong><\/strong><\/p>\n<\/section>\n

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Only mimic-species can survive when external noises are added in a ratio-dependent community dynamics model<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00111-2<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5206\u754c\u7ebf\uff08\u6d0b\u7ea2\u8272\u7ebf\uff09\u548c\u7f6e\u4fe1\u692d\u5706\uff08\u5b9e\u7ebf\uff09<\/span><\/p>\n


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\u672c\u6587\u8ba8\u8bba\u4e86\u7a33\u5b9a\u5185\u5e73\u8861\u70b9\u5438\u5f15\u76c6\u5730\u4e2d\u566a\u58f0\u8bf1\u5bfc\u8f6c\u53d8\u7684\u673a\u7406\u3002\u5e94\u7528\u968f\u673a\u7075\u654f\u5ea6\u51fd\u6570\u6280\u672f\u6784\u9020\u4e86\u7a33\u5b9a\u5185\u5e73\u8861\u70b9\u9644\u8fd1\u7684\u7f6e\u4fe1\u57df\uff0c\u5e76\u7814\u7a76\u4e86\u4e0d\u540c\u566a\u58f0\u5f3a\u5ea6\u4e0b\u7684\u8fc7\u6e21\u3002<\/span><\/p>\n


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19. \u6709\u9650\u89c4\u6a21\u6548\u5e94\u3001\u4eba\u53e3\u7edf\u8ba1\u566a\u58f0<\/strong><\/strong><\/p>\n

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Finite-size effects, demographic noise, and ecosystem dynamics<\/span>
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\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00184-z<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5f3a\u6b63\u53cd\u9988\u88ab\u8ba4\u4e3a\u662f\u89c2\u5bdf\u751f\u6001\u7cfb\u7edf\u7a81\u53d8\u7684\u5fc5\u8981\u6761\u4ef6\u3002\u4e4b\u524d\u7684\u4e00\u4e9b\u7814\u7a76\u5df2\u7ecf\u8868\u660e\uff0c\u4eba\u53e3\u566a\u58f0<\/span>\uff08demographic noise\uff0c\u7531\u6709\u9650\u7cfb\u7edf\u4e2d\u51fa\u751f\u548c\u6b7b\u4ea1\u8fc7\u7a0b\u7684\u6982\u7387\u6027\u548c\u79bb\u6563\u6027\u4ea7\u751f\u7684\u566a\u58f0\uff0c\u4e5f\u79f0\u4eba\u53e3\u7edf\u8ba1\u566a\u58f0\uff09<\/span>\u4f1a\u4f7f\u8fc7\u6e21\u9010\u6e10\u53d1\u751f\u3002\u672c\u6587\u7814\u7a76\u4e86\u4eba\u53e3\u566a\u58f0\u5bf9\u6709\u9650\u751f\u6001\u7cfb\u7edf\u7684\u5f71\u54cd\u3002\u7814\u7a76\u8005\u4f7f\u7528\u4e00\u4e2a\u7b80\u5355\u7684\u7ec6\u80de\u81ea\u52a8\u673a\u6a21\u578b\uff0c\u51fa\u751f\u548c\u6b7b\u4ea1\u53d7\u6b63\u53cd\u9988\u8fc7\u7a0b\u7684\u5f71\u54cd\u3002\u7814\u7a76\u8005\u4ee5\u7c7b\u4f3c\u6559\u7a0b\u7684\u683c\u5f0f\u5c55\u793a\u7814\u7a76\u8005\u7684\u65b9\u6cd5\u3002\u5229\u7528van Kampen\u7684\u7cfb\u7edf\u89c4\u6a21\u6269\u5c55\u65b9\u6cd5\uff0c\u7814\u7a76\u8005\u5bfc\u51fa\u4e86\u4e00\u4e2a\u63cf\u8ff0\u6709\u9650\u7cfb\u7edf\u4e2d\u5c40\u90e8\u6982\u7387\u89c4\u5219\u5982\u4f55\u6269\u5c55\u5230\u968f\u673a\u79cd\u7fa4\u52a8\u529b\u5b66\u7684\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u3002<\/span><\/p>\n


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\u6a21\u578b\u66f4\u65b0\u89c4\u5219\u793a\u610f\u56fe\u3002\u5de6\u9762\u677f\u663e\u793a\u4e86\u5f53\u7126\u70b9\u690d\u7269\u7684\u76f8\u90bb\u7ad9\u70b9\u4e3a\u7a7a\u65f6\uff0c\u6240\u5b9e\u65bd\u7684\u57fa\u7ebf\u590d\u5236\u8fc7\u7a0b\u3002\u53f3\u56fe\u663e\u793a\u4e86\u5f53\u7126\u70b9\u690d\u7269\u7684\u90bb\u8fd1\u5730\u70b9\u88ab\u5360\u7528\u65f6\u5b9e\u65bd\u7684\u6b63\u53cd\u9988\u8fc7\u7a0b\u3002<\/span><\/section>\n


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\u7814\u7a76\u8005\u8bc1\u660e\uff0c\u4f5c\u4e3a\u4eba\u53e3\u566a\u58f0\u589e\u5f3a\u7684\u7ed3\u679c\uff0c\u6709\u9650\u89c4\u6a21\u7684\u751f\u6001\u7cfb\u7edf\u53ef\u4ee5\u663e\u793a\u4e00\u4e2a\u201c\u6709\u6548\u7684\u7a81\u53d8\u201d\uff0c\u5373\u4f7f\u6709\u5fae\u5f31\u7684\u6b63\u4ea4\u4e92\u4f5c\u7528\u3002\u7814\u7a76\u8005\u7684\u7a7a\u95f4\u663e\u5f0f\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df\u8bc1\u5b9e\u4e86\u8fd9\u79cd\u5206\u6790\u9884\u671f\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u8005\u9884\u6d4b\uff0c\u5c0f\u89c4\u6a21\u7684\u79cd\u7fa4\u548c\u751f\u6001\u7cfb\u7edf\uff0c\u5728\u5bf9\u73af\u5883\u9a71\u52a8\u56e0\u7d20\u7684\u53cd\u5e94\u4e2d\u5f88\u5bb9\u6613\u7a81\u7136\u5d29\u6e83\uff1b\u800c\u8f83\u5927\u7684\u7cfb\u7edf\u2014\u2014\u5177\u6709\u76f8\u540c\u7684\u5fae\u89c2\u76f8\u4e92\u4f5c\u7528\u2014\u2014\u5219\u8868\u73b0\u51fa\u5e73\u7a33\u7684\u53cd\u5e94\u3002<\/span><\/p>\n


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20. \u5229\u7528\u903b\u8f91\u64cd\u4f5c\u7684\u4e34\u754c\u70b9<\/strong><\/strong><\/p>\n<\/section>\n

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Harnessing tipping points for logic operations<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/link.springer.com\/article\/10.1140\/epjs\/s11734-021-00014-2<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u7814\u7a76\u8005\u9996\u5148\u56de\u987e\u5229\u7528\u6df7\u6c8c\u5438\u5f15\u5b50\u6765\u5b9e\u73b0\u7075\u6d3b\u5e76\u7a33\u5065\u7684\u903b\u8f91\u95e8\u7684\u60f3\u6cd5\uff0c\u5e76\u5728\u7a81\u53d8\u70b9\u7684\u80cc\u666f\u4e0b\u91cd\u65b0\u5b9a\u4e49\u8fd9\u4e9b\u6982\u5ff5\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f:\u590d\u6742\u7cfb\u7edf\u4e2d\u7a81\u53d8\u70b9\u7684\u5b58\u5728\u4f7f\u5176\u5177\u6709\u5728\u53c2\u6570\u53d8\u5316\u5f88\u5c0f\u7684\u60c5\u51b5\u4e0b\u5728\u975e\u5e38\u4e0d\u540c\u7684\u5438\u5f15\u5b50\u4e4b\u95f4\u5207\u6362\u7684\u80fd\u529b\uff0c\u5229\u7528\u8fd9\u4e00\u7279\u6027\u53ef\u4ee5\u83b7\u5f97\u53ef\u9760\u7684\u903b\u8f91\u8fd0\u7b97\u3002\u4e8c\u8fdb\u5236\u903b\u8f91\u8f93\u51fa\u53ef\u4ee5\u6709\u6548\u5730\u6620\u5c04\u5230\u4e0d\u540c\u76f8\u7a7a\u95f4\u533a\u57df\u5185\u7684\u52a8\u6001\u5438\u5f15\u5b50\uff0c\u903b\u8f91\u8f93\u5165\u53ef\u4ee5\u901a\u8fc7\u53c2\u6570\u7684\u5fae\u5c0f\u53d8\u5316\u8fdb\u884c\u7b80\u5355\u7684\u7f16\u7801\u3002\u7136\u540e\uff0c\u7814\u7a76\u8005\u7ee7\u7eed\u7528\u591a\u8f93\u5165\u903b\u8f91\u64cd\u4f5c\u7684\u65b0\u5b9e\u73b0\u6765\u6269\u5c55\u7814\u7a76\u8005\u7684\u4e2d\u5fc3\u601d\u60f3\u3002<\/span><\/p>\n


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\u9762\u677f\u4ece\u4e0a\u5230\u4e0b\u663e\u793a\u8f93\u5165\u6d41 I1 \u548c I2\uff08\u5f53\u903b\u8f91\u8f93\u5165\u4e3a 0 \u65f6\u53d6\u503c\u4e3a -0.002\uff0c\u5f53\u903b\u8f91\u8f93\u5165\u4e3a 1 \u65f6\u53d6\u503c\u4e3a 0.002\uff09\u548c x(t)\uff08\u7ea2\u8272\uff09\u6e05\u695a\u5730\u663e\u793a\u903b\u8f91 OR \u8f93\u51fa\uff08x(t )>0 \u4e3a\u903b\u8f91\u8f93\u51fa 1\uff0cx(t)<0 \u4e3a\u903b\u8f91\u8f93\u51fa 0)\u3002\u72b6\u6001\u53d8\u91cf y(t)\uff08\u7eff\u8272\uff09\u5e76\u884c\u4ea7\u751f\u4e92\u8865\u7684 NOR \u903b\u8f91\u95e8\u54cd\u5e94\u3002\u5176\u4e2d\uff0cA=0.11\uff0c\u03c9=0.74\uff0cb=0.002<\/span><\/section>\n


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\u7814\u7a76\u8005\u660e\u786e\u5730\u5c55\u793a\u4e86\u7cfb\u7edf\u5728\u54cd\u5e94\u591a\u4e2a\u8f93\u5165\u7684\u5916\u90e8\u6d41\u65f6\u4e00\u81f4\u5730\u8df3\u8f6c\uff0c\u4ece\u800c\u63d0\u4f9b\u4e86\u66f4\u590d\u6742\u7684\u591a\u8f93\u5165\u903b\u8f91\u95e8\u7684\u5065\u58ee\u5b9e\u73b0\u3002\u7814\u7a76\u8005\u8bc1\u660e\u4e86\u7a81\u53d8\u70b9\u7684\u5b58\u5728\u63d0\u4f9b\u4e86\u4e00\u4e2a\u4f18\u52bf\uff0c\u5373\u975e\u5e38\u4f4e\u7684\u632f\u5e45\u8f93\u5165\u53ef\u4ee5\u4ea7\u751f\u9ad8\u5ea6\u653e\u5927\u7684\u8f93\u51fa\u3002\u7814\u7a76\u8005\u8fd8\u8bc1\u660e\u566a\u58f0\u53ef\u4ee5\u53d1\u6325\u5efa\u8bbe\u6027\u7684\u4f5c\u7528\uff0c\u63d0\u9ad8\u7d27\u6025\u591a\u8f93\u5165\u903b\u8f91\u8fd0\u7b97\u7684\u53ef\u9760\u6027\uff0c\u4ece\u800c\u52a0\u5f3a\u5e7f\u4e49\u903b\u8f91\u968f\u673a\u5171\u632f\u7684\u6982\u5ff5\u3002\u8fd9\u4e9b\u7ed3\u679c\u8868\u660e\uff0c\u7a81\u53d8\u673a\u5236\u53ef\u4ee5\u7528\u4e8e\u6784\u9020\u901a\u7528\u8ba1\u7b97\u8bbe\u5907\uff0c\u901a\u8fc7\u5fae\u5c0f\u7684\u53c2\u6570\u53d8\u5316\u5c31\u80fd\u6709\u6548\u5730\u91cd\u65b0\u914d\u7f6e\u903b\u8f91\u529f\u80fd\u3002<\/span><\/p>\n


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21. \u70ed\u58f0\u7cfb\u7edf\u4e2d\u7684\u4e34\u754c\u8f6c\u53d8\u53ca\u5176\u9884\u8b66\u4fe1\u53f7<\/strong><\/strong><\/p>\n<\/section>\n

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Critical transitions and their early warning signals in thermoacoustic systems<\/span><\/h3>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

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