{"id":40735,"date":"2023-02-15T20:35:17","date_gmt":"2023-02-15T12:35:17","guid":{"rendered":"https:\/\/swarma.org\/?p=40735"},"modified":"2023-02-15T20:35:17","modified_gmt":"2023-02-15T12:35:17","slug":"physics-reports%e9%87%8d%e7%a3%85%e7%bb%bc%e8%bf%b0%ef%bc%9a%e7%bd%91%e7%bb%9c%e9%9f%a7%e6%80%a7%e5%8f%8a%e6%a0%b8%e5%bf%83%e7%a0%94%e7%a9%b6%e4%b8%bb%e9%a2%98","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=40735","title":{"rendered":"Physics Reports\u91cd\u78c5\u7efc\u8ff0\uff1a\u7f51\u7edc\u97e7\u6027\u53ca\u6838\u5fc3\u7814\u7a76\u4e3b\u9898"},"content":{"rendered":"
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\u8bb8\u591a\u7cfb\u7edf\u4e00\u65e6\u8d8a\u8fc7\u201c\u4e34\u754c\u70b9\u201d\uff0c\u5176\u72b6\u6001\u5c06\u4f1a\u53d1\u751f\u4e0d\u53ef\u9006\u7684\u6539\u53d8\uff0c\u5e76\u5e26\u6765\u4e25\u91cd\u5371\u5bb3\u3002\u201c\u97e7\u6027\u201d\u53cd\u6620\u4e86\u7cfb\u7edf\u907f\u514d\u72b6\u6001\u8f6c\u53d8\u6216\u4ece\u975e\u5e38\u6001\u4e2d\u5feb\u901f\u6062\u590d\u7684\u80fd\u529b\uff0c\u5b83\u4f7f\u7cfb\u7edf\u80fd\u5728\u6545\u969c\u6216\u6270\u52a8\u53d1\u751f\u65f6\u8c03\u6574\u5176\u6d3b\u52a8\u4ee5\u7ef4\u6301\u57fa\u672c\u529f\u80fd\u3002\u5728\u8fc7\u53bb50\u5e74\u91cc\uff0c\u4eba\u4eec\u51e0\u4e4e\u53ea\u5173\u6ce8\u4f4e\u7ef4\u7cfb\u7edf\u97e7\u6027\u3002\u968f\u7740\u7f51\u7edc\u79d1\u5b66\u7406\u8bba\u7684\u53d1\u5c55\uff0c\u5b66\u8005\u4eec\u9010\u6e10\u5f00\u59cb\u63a2\u7d22\u771f\u5b9e\u4e16\u754c\u4e2d\u590d\u6742\u7684\u591a\u7ef4\u7f51\u7edc\u7cfb\u7edf\u53ca\u5176\u97e7\u6027\u3002<\/span><\/strong>2022\u5e74\uff0cPhysics Reports <\/em>\u53d1\u8868\u7efc\u8ff0\u6587\u7ae0 Network <\/span>Resilience \u5168\u9762\u5730\u56de\u987e\u4e86\u7f51\u7edc\u97e7\u6027\u7684\u7814\u7a76\u65b9\u6cd5\uff0c\u53ca\u5176\u5728\u751f\u6001\u3001\u751f\u7269\u3001\u793e\u4f1a\u548c\u57fa\u7840\u8bbe\u65bd\u7b49\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\uff0c\u5e76\u5c55\u671b\u4e86\u672a\u6765\u7f51\u7edc\u97e7\u6027\u7814\u7a76\u7684\u65b9\u5411\u4e0e\u6311\u6218\u3002\u672c\u6587\u662f\u5bf9\u8be5\u7efc\u8ff0\u7684\u57fa\u7840\u7406\u8bba\u548c\u65b9\u6cd5\u7684\u7b80\u4ecb\u3002<\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

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\u751f\u6d3b\u4e2d\u96be\u4ee5\u9884\u77e5\u7684\u6270\u52a8\u65e0\u5904\u4e0d\u5728\uff0c\u5c0f\u5230\u4e2a\u4eba\u7684\u611f\u5192\u53d1\u70e7\u6216\u60c5\u7eea\u5931\u843d\uff0c\u5927\u5230\u57fa\u7840\u8bbe\u65bd\u762b\u75ea\u6216\u7269\u79cd\u706d\u7edd\u3002\u8003\u8651\u5230\u6270\u52a8\u5e26\u6765\u7684\u8d1f\u9762\u540e\u679c\uff0c\u4eba\u4eec\u8d8a\u6765\u8d8a\u5173\u6ce8\u7cfb\u7edf\u5e94\u5bf9\u6270\u52a8\u7684\u97e7\u6027<\/span>\uff08resilience\uff09<\/span>\u3002resilience\u8d77\u6e90\u4e8e\u62c9\u4e01\u8bed\u4e2d\u7684 resiliere \u6216 resilio\uff0c\u5206\u522b\u8868\u793a\u201c\u53cd\u5f39\u201d\u6216 \u201c\u56de\u5f39\u201d[1]\uff0c\u6240\u4ee5\u97e7\u6027\u53c8\u88ab\u79f0\u4e3a\u5f39\u6027\u3001\u6062\u590d\u529b\u7b49\u3002\u97e7\u6027\u5728\u751f\u6001\u3001\u91d1\u878d\u3001\u4ea4\u901a\u7b49\u591a\u4e2a\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u5e94\u7528\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u7cfb\u7edf\u5728\u9762\u5bf9\u6270\u52a8\u4e8b\u4ef6\u65f6\u7684\u53cd\u5e94\uff0c\u6216\u7cfb\u7edf\u8c03\u6574\u5176\u884c\u4e3a\u6d3b\u52a8\u4ee5\u7ef4\u6301\u57fa\u672c\u529f\u80fd\u7684\u80fd\u529b<\/strong>\u3002\u867d\u7136\u4e0d\u540c\u5b66\u79d1\u9886\u57df\u4e2d\u7684\u97e7\u6027\u5173\u6ce8\u70b9\u4e0d\u5c3d\u76f8\u540c\uff0c\u4f46\u5404\u9886\u57df\u4e13\u4e1a\u6280\u53d6\u957f\u8865\u77ed\u5171\u540c\u63a8\u52a8\u7740\u97e7\u6027\u7814\u7a76\u7684\u8fdb\u6b65\u3002<\/span><\/section>\n

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\u56fe1. \u7ecf\u5386\u5c71\u706b\u540e\u679d\u5e72\u91cd\u65b0\u957f\u51fa\u5ae9\u53f6\u3002<\/span><\/section>\n

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\u7531\u4e8e\u7cfb\u7edf\u9762\u5bf9\u6270\u52a8\u53cd\u5e94\u7684\u591a\u6837\u6027\u548c\u590d\u6742\u6027\uff0c\u76ee\u524d\u4ecd\u672a\u6709\u97e7\u6027\u7684\u7edf\u4e00\u5b9a\u4e49\u3002\u56de\u987e\u8fc7\u5f80\u7814\u7a76\u91cc70\u591a\u79cd\u97e7\u6027\u5b9a\u4e49[2]\uff0c\u5927\u591a\u6570\u5b9a\u4e49\u90fd\u56f4\u7ed5\u4ee5\u4e0b\u4e09\u7c7b\u97e7\u6027\uff1a\uff081\uff09\u7cfb\u7edf\u97e7\u6027<\/strong><\/span> (system resilience)<\/span>\uff0c\u53c8\u79f0\u751f\u6001\u97e7\u6027\uff0c\u4e3b\u8981\u5173\u6ce8\u7cfb\u7edf\u5728\u4e0d\u8f6c\u79fb\u5230\u53e6\u4e00\u7a33\u5b9a\u72b6\u6001\u60c5\u51b5\u4e0b\u6240\u80fd\u627f\u53d7\u7684\u6700\u5927\u6270\u52a8\u7a0b\u5ea6[3]\u3002\uff082\uff09\u5de5\u7a0b\u97e7\u6027<\/strong><\/span> (engineering resilience) <\/span>\u91cd\u70b9\u5173\u6ce8\u6270\u52a8\u540e\u7684\u6062\u590d\u901f\u7387\u6216\u65f6\u95f4[4]\u3002\uff083\uff09\u9002\u5e94\u6027\u97e7\u6027<\/strong><\/span> (adaptive resilience) <\/span>\u591a\u7528\u4e8e\u63cf\u8ff0\u793e\u4f1a\u7cfb\u7edf\u5bf9\u610f\u5916\u548c\u6781\u7aef\u51b2\u51fb\u7684\u9002\u5e94\u548c\u8f6c\u53d8\u80fd\u529b[28]\u3002<\/span><\/section>\n

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\u5728\u8fc7\u53bb\u51e0\u5341\u5e74\u91cc\uff0c\u7531\u4e8e\u7f3a\u5c11\u5927\u89c4\u6a21\u7cfb\u7edf\u4e2d\u7684\u5185\u5728\u52a8\u529b\u5b66\u4fe1\u606f\u548c\u9ad8\u6548\u7684\u5206\u6790\u5de5\u5177\uff0c\u5927\u591a\u6570\u7814\u7a76\u4e3b\u8981\u96c6\u4e2d\u4e8e\u4f4e\u7ef4\u7cfb\u7edf\u6216\u65f6<\/strong><\/span>\u95f4\u5e8f\u5217\u6570\u636e\u7684\u5206\u6790<\/strong>[5,6,7]\u3002\u5982\u56fe2\u6240\u793a\uff0c\u5728\u52a8\u529b\u5b66\u6a21\u578b\u4e2d\uff0c\u97e7\u6027\u884c\u4e3a\u53ef\u4ee5\u88ab\u63cf\u8ff0\u4e3a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u65b9\u7a0b<\/span>\uff1a<\/span>dx\/dt=f(\u03b2<\/span>, x)\uff0c\u5176\u4e2df(\u03b2<\/span>, x)<\/span>\u8868\u793a\u7cfb\u7edf\u52a8\u529b<\/span>\u5b66\uff0c\u03b2<\/span>\u8868\u793a<\/span>\u73af\u5883\u72b6\u6001\u3002<\/span><\/section>\n

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\u56fe2. \u4e00\u7ef4\u7cfb\u7edf\u7684\u97e7\u6027\u3002\uff08A\uff09\u5f53<\/span>\u03b2<\/span>\uff1e\u03b2<\/span><\/span>c<\/sub>\uff08\u84dd\u8272\uff09\u65f6\uff0c\u7cfb\u7edf\u53ea\u6709\u4e00\u4e2a\u7a33\u6001\uff08stable fixed point\uff09\uff0c\u5426\u5219\u4f1a\u51fa\u73b0\u4e24\u4e2a\uff08\u6216\u66f4\u591a\uff09\u7a33\u6001\u3002\uff08B\uff09\u5177\u6709\u4ece\u79ef\u6781\uff08\u84dd\u8272\uff09\u72b6\u6001\u5230\u8d1f\u9762\uff08\u7ea2\u8272\uff09\u72b6\u6001\u7684\u4e00\u9636\u8dc3\u8fc1\u7684\u97e7\u6027\u51fd\u6570\u3002\uff08C\uff09\u97e7\u6027\u51fd\u6570\u5728\u03b2<\/span><\/span>\uff1c\u03b2<\/span><\/span>c<\/sub><\/span>\u65f6\u6709\u7a33\u5b9a\u89e3\uff0c\u5927\u4e8e\u03b2<\/span><\/span>c<\/sub><\/span><\/span>\u65f6\u65e0\u89e3\u3002<\/span><\/p>\n


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\u63d0\u53d6\u590d\u6742\u7cfb\u7edf\u7684\u97e7\u6027\u51fd\u6570\u9700\u8981\u638c\u63e1\u5143\u7d20\u4e4b\u95f4\u590d\u6742\u76f8\u4e92\u4f5c\u7528\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7279\u5f81\uff0c\u800c\u7f51\u7edc\u79d1\u5b66\u7684\u51fa\u73b0\u4e3a\u63cf\u8ff0\u5927\u89c4\u6a21\u771f\u5b9e\u7cfb\u7edf\u4e2d\u7684\u7ed3\u6784\u63d0\u4f9b\u4e86\u5f3a\u6709\u529b\u7684\u5de5\u5177[8]\u3002\u6b64\u5916\uff0c\u6d77\u91cf\u6570\u636e\u548c\u7b97\u6cd5\u53d1\u5c55\u4f7f\u5f97\u4eba\u4eec\u53ef\u4ee5\u76f4\u63a5\u4ece\u5386\u53f2\u6570\u636e\u8bc6\u522b\u5e76\u9884\u6d4b\u52a8\u6001\u6a21\u578b\u7684\u51c6\u786e\u5f62\u5f0f[9,10]\u3002\u5728\u7406\u8bba\u3001\u6570\u636e\u548c\u6280\u672f\u591a\u65b9\u652f\u6301\u4e0b\uff0c\u7f51\u7edc\u97e7\u6027 (network resilience) \u4f5c\u4e3a\u5206\u6790\u9ad8\u7ef4\u7cfb\u7edf\u97e7\u6027\u7684\u5de5\u5177\u5e94\u8fd0\u800c\u751f\u3002<\/strong><\/span><\/section>\n

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1973\u5e74\uff0cHolling\u7b49\u4eba[11]\u5c06\u97e7\u6027\u5b9a\u4e49\u4e3a\u7cfb\u7edf\u7684\u6301\u4e45\u6027\uff0c\u53ca\u5176\u5438\u6536\u6270\u52a8\u548c\u53d8\u5316\u7684\u80fd\u529b\u3002\u540e\u6765\uff0c\u97e7\u6027\u4f5c\u4e3a\u4e00\u4e2a\u901a\u7528\u6982\u5ff5\u5e7f\u6cdb\u5e94\u7528\u4e8e\u751f\u7269\u5b66[12]\u3001\u793e\u4f1a\u79d1\u5b66[13]\u548c\u5de5\u7a0b\u5b66[14]\u4e2d\u3002\u7cfb\u7edf\u97e7\u6027\u51b3\u5b9a\u4e86\u7cfb\u7edf\u662f\u5426\u80fd\u591f\u5bb9\u5fcd\u663e\u8457\u7684\u6270\u52a8\u800c\u4e0d\u8f6c\u79fb\u5230\u53e6\u4e00\u4e2a\u7a33\u5b9a\u72b6\u6001\uff0c\u8861\u91cf\u4e86\u7cfb\u7edf\u5438\u6536\u72b6\u6001\u53d8\u91cf\u3001\u9a71\u52a8\u53d8\u91cf\u548c\u53c2\u6570\u53d8\u5316\u5e76\u4fdd\u6301\u4e0d\u53d8\u7684\u80fd\u529b[15]\u3002\u6b63\u5982\u524d\u6587\u6240\u4ecb\u7ecd\u7684\uff0c\u4ece\u751f\u6001\u5b66\u5230\u5de5\u7a0b\u5b66\u6240\u4f7f\u7528\u7684\u97e7\u6027\u4f20\u7edf\u6570\u5b66\u5904\u7406\u65b9\u5f0f\u4e3a\uff1a\u7528\u4e00\u7ef4\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u65b9\u7a0bdx<\/span>\/dt<\/span>=<\/span>f(<\/span>\u03b2<\/span>,<\/span> x<\/span>)<\/span><\/span>\u6765\u8fd1\u4f3c\u590d\u6742\u7cfb\u7edf\u7684\u884c\u4e3a\uff0c\u6355\u6349\u97e7\u6027\u76f8\u5173\u7684\u5173\u952e\u72b6\u6001\u53d8\u5316\u3002<\/span><\/section>\n

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\u7136\u800c\uff0c\u73b0\u5b9e\u4e16\u754c\u4e2d\u7684\u7cfb\u7edf\u662f\u7531\u8bb8\u591a\u5143\u7d20\u901a\u8fc7\u590d\u6742\u7684\u52a0\u6743\u6709\u5411\u76f8\u4e92\u4f5c\u7528\u5173\u7cfb\u7ec4\u6210\u7684\uff0c\u5e76\u4e14\u53d7\u5927\u91cf\u53c2\u6570\u63a7\u5236\u3002\u56e0\u6b64\u5b83\u4eec\u7684\u72b6\u6001\u4e0d\u80fd\u4ec5\u9760\u4e00\u7ef4\u65b9\u7a0b\u63cf\u8ff0\uff0c\u800c\u662f\u9700\u8981\u7531\u7f51\u7edc\u5f62\u5f0f\u7684\u8026\u5408\u975e\u7ebf\u6027\u65b9\u7a0b\u6765\u6355\u6349\u7cfb\u7edf\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5173\u7cfb\uff0c\u5e76\u63ed\u793a\u7cfb\u7edf\u52a8\u529b\u5b66\u548c\u5e95\u5c42\u7f51\u7edc\u62d3\u6251\u53d8\u5316\u4e4b\u95f4\u7684\u590d\u6742\u76f8\u4e92\u4f5c\u7528<\/strong>\u3002\u56e0\u6b64 \uff0c\u6240\u5f97\u5230\u7684\u97e7\u6027\u51fd\u6570\u662f\u8868\u5f81\u7cfb\u7edf\u590d\u6742\u53c2\u6570\u7a7a\u95f4\u4e0a\u7684\u591a\u7ef4\u6d41\u5f62\u3002\u82e5\u8981\u5c06\u4e00\u7ef4\u7cfb\u7edf\u97e7\u6027\u62d3\u5c55\u5230\u7f51\u7edc\u97e7\u6027\uff0c\u9700\u8981\u7406\u89e3\u548c\u56de\u987e\u4ee5\u4e0b\u4e09\u65b9\u9762\u5185\u5bb9\uff1a<\/span><\/p>\n

\uff081\uff09  \u7f51\u7edc\u4e2d\u591a\u7ef4\u52a8\u529b\u5b66\u65b9\u7a0b\uff1b<\/span><\/p>\n

\uff082\uff09  \u9ad8\u7ef4\u7cfb\u7edf\u7684\u97e7\u6027\u73b0\u8c61\u548c\u53ef\u80fd\u7684\u4e34\u754c\u8f6c\u53d8\uff1b<\/span><\/p>\n

\uff083\uff09  \u9002\u7528\u4e8e\u7f51\u7edc\u5404\u79cd\u97e7\u6027\u529f\u80fd\u7684\u5206\u6790\u5de5\u5177\u3002<\/span><\/section>\n


<\/h3>\n

2.1 \u7f51\u7edc\u52a8\u529b\u5b66\u5efa\u6a21<\/span><\/strong><\/span><\/h3>\n

<\/section>\n
\u7f51\u7edc\u52a8\u529b\u5b66\u63cf\u8ff0\u4e86\u7f51\u7edc\u5bf9\u8c61\u7684\u8fdb\u5316\u8fc7\u7a0b\uff0c\u4f8b\u5982\u4e00\u6bb5\u65f6\u95f4\u5185\u7684\u7269\u79cd\u4e30\u5bcc\u5ea6\u5982\u4f55\u8fdb\u5316[16]\u3001\u4e2a\u4f53\u5728\u6d41\u884c\u75c5\u4f20\u64ad\u8fc7\u7a0b\u4e2d\u7684\u611f\u67d3\u72b6\u6001[17]\u7b49\u7b49\u3002\u7531\u4e8e\u8be5\u8fc7\u7a0b\u5145\u6ee1\u590d\u6742\u6027\u548c\u672a\u77e5\u6027\uff0c\u786e\u5b9a\u5176\u65b9\u7a0b\u5f62\u5f0f\u4e0e\u53c2\u6570\u5e76\u4e0d\u5bb9\u6613\u3002\u4e0e\u73b0\u6709\u7684\u5927\u91cf\u7f51\u7edc\u9759\u6001\u7ed3\u6784\u5efa\u6a21\u7814\u7a76\u76f8\u6bd4[18]\uff0c\u5bf9\u5927\u89c4\u6a21\u7f51\u7edc\u52a8\u6001\u5efa\u6a21\u7684\u7814\u7a76\u4ecd\u7136\u8f83\u5c11\u3002\u4e0b\u9762\u56de\u987e\u51e0\u4e2a\u7ecf\u5178\u7684\u5927\u89c4\u6a21\u7cfb\u7edf\u7684\u52a8\u6001\u6a21\u578b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u27a2 \u7cfb\u7edf\u53ef\u80fd\u8868\u73b0\u51fa\u5404\u79cd\u975e\u7ebf\u6027\u52a8\u529b\u5b66[19,20]\uff0c\u5982\u632f\u8361\u3001\u6269\u6563\u548c\u5206\u5c94\uff0c\u8fd9\u4e9b\u52a8\u6001\u6a21\u578b\u6d89\u53ca\u4e0d\u540c\u7684\u65b9\u7a0b\u5f62\u5f0f\u548c\u53c2\u6570\u3002\u4f8b\u5982\uff0c\u7f51\u7edc\u5316\u7684Stuart\u2013Landau (SL) \u632f\u8361\u5668\u7cfb\u7edf[21]\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u8026\u5408\u7684\u5e38\u5fae\u5206\u65b9\u7a0b<\/span> (ODEs) <\/span>\u6765\u63cf\u8ff0\uff1a<\/span><\/section>\n
<\/section>\n
\u27a2 \u57fa\u56e0\u8c03\u63a7\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u53ef\u4ee5\u5efa\u6a21\u4e3a\u7c73\u6c0f\u65b9\u7a0b<\/span> (Michaelis\u2013Menten equations)<\/span>[22]\uff1a<\/span><\/section>\n

<\/p>\n

\u27a2 \u7f51\u7edc\u4f20\u64ad\u8fc7\u7a0b\u53ef\u4ee5\u88ab\u5efa\u6a21\u4e3a\u7ecf\u5178\u7684SIS\u6a21\u578b<\/span> (susceptible infected susceptible model)<\/span>[23]\uff1a<\/span><\/section>\n

<\/p>\n

\u27a2 \u6240\u6709\u8fd9\u4e9b\u52a8\u529b\u5b66\u65b9\u7a0b\u5199\u6210\u4ee5\u4e0b\u7684\u666e\u9002\u5f62\u5f0f\uff1a<\/span><\/section>\n

<\/p>\n

\u5176\u4e2d\u7b2c\u4e00\u9879W(xi<\/sub>(t))<\/span>\u63cf\u8ff0x<\/span>i<\/sub><\/span>\u7684\u81ea\u6211\u9a71\u52a8<\/span> (self-dynamics)<\/span>\uff0c\u7b2c\u4e8c\u9879\u53cd\u6620i<\/span>\u548c\u90bb\u5c45\u4e2a\u4f53\u7684\u4f5c\u7528\u5173\u7cfb\u3002\u957f\u671f\u4ee5\u6765\uff0c\u5927\u89c4\u6a21\u7f51\u7edc\u7684\u97e7\u6027\u9884\u6d4b\u4e00\u76f4\u53d7\u5230\u7f51\u7edc\u5185\u90e8\u590d\u6742\u4f5c\u7528\u7684\u9650\u5236\u3002\u5c3d\u7ba1\u76ee\u524d\u5bf9\u4e8e\u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u7684\u53d1\u73b0\u4ecd\u662f\u4e00\u4e2a\u91cd\u5927\u6311\u6218\uff0c\u4f46\u4f7f\u7528\u4e0a\u8ff0\u65b9\u6cd5\u6765\u63a8\u65ad\u7f51\u7edc\u52a8\u529b\u5b66\uff0c\u6709\u53ef\u80fd\u5b9e\u73b0\u5bf9\u5927\u89c4\u6a21\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u5efa\u6a21\uff0c\u4ece\u800c\u6784\u5efa\u7f51\u7edc\u97e7\u6027\u5206\u6790\u7684\u57fa\u672c\u6846\u67b6\u3002<\/span><\/section>\n

<\/span><\/section>\n

2.2 \u52a8\u529b\u7cfb\u7edf\u4e2d\u7684\u97e7\u6027\u73b0\u8c61<\/span><\/strong><\/span><\/h3>\n

<\/span><\/section>\n
\u52a8\u529b\u7cfb\u7edf\u7684\u72b6\u6001\u53ef\u80fd\u968f\u7740\u5916\u90e8\u6761\u4ef6\u53d8\u5316\u800c\u53d8\u5316\uff0c\u4e14\u54cd\u5e94\u901a\u5e38\u662f\u660e\u663e\u7684\u3002\u56fe3\u5c55\u793a\u4e86\u4e0d\u540c\u7c7b\u578b\u7684\u7cfb\u7edf\u72b6\u6001\u54cd\u5e94\u66f2\u7ebf\u3002\u5f53\u5916\u90e8\u6761\u4ef6\u968f\u65f6\u95f4\u9010\u6e10\u53d8\u5316\u65f6[24]\uff0c\u4e00\u4e9b\u9ad8\u97e7\u6027\u7cfb\u7edf\u7684\u72b6\u6001\u53ef\u80fd\u4f1a\u5448\u7ebf\u6027\u54cd\u5e94<\/span>\uff08\u89c1\u56fe3A\uff09<\/span>\u3002\u66f4\u5e38\u89c1\u4e14\u66f4\u590d\u6742\u7684\u54cd\u5e94\u5173\u7cfb\u662f\u975e\u7ebf\u6027\u7684\uff0c\u968f\u7740\u63a7\u5236\u53c2\u6570\u589e\u52a0\uff0c\u51fa\u73b0\u201c\u4ece\u4e0a\u81f3\u4e0b\u201d\u8fde\u7eed\u4e14\u8fc7\u6e21\u7684\u76f8\u53d8<\/span>\uff08\u89c1\u56fe3B\uff09<\/span>\u3002\u5728\u7ebf\u6027\u548c\u8fde\u7eed\u7684\u975e\u7ebf\u6027\u60c5\u51b5\u4e0b\uff0c\u90fd\u53ea\u5b58\u5728\u4e00\u4e2a\u5e73\u8861\u72b6\u6001\u3002\u5f53\u63a7\u5236\u53c2\u6570\u6062\u590d\u5230\u539f\u5148\u6c34\u5e73\uff0c\u7cfb\u7edf\u4e5f\u53ef\u4ee5\u6062\u590d\u5230\u4e4b\u524d\u7684\u72b6\u6001[25,26]\u3002\u4e00\u4e9b\u7cfb\u7edf\u53ef\u80fd\u5728\u7279\u5b9a\u7684\u6761\u4ef6\u8303\u56f4\u5185\u201c\u53cd\u5e94\u8fdf\u949d\u201d\uff0c\u800c\u5728\u63a7\u5236\u53c2\u6570\u63a5\u8fd1\u67d0\u9608\u503c\u65f6\u7a81\u7136\u54cd\u5e94\uff0c\u5728\u4e24\u4e2a\u72ec\u7acb\u7684\u72b6\u6001\u4e4b\u95f4\u8868\u73b0\u51fa\u610f\u60f3\u4e0d\u5230\u7684\u72b6\u6001\u8f6c\u79fb<\/span>\uff08\u89c1\u56fe3C\uff09<\/span>\u3002\u4ee5\u4e0a\u4e09\u79cd\u7c7b\u578b\u7684\u72b6\u6001\u53d8\u5316\u79f0\u4e3a\u76f8\u53d8 (phase shift) <\/strong>\u6216\u7a33\u6001\u8f6c\u79fb (regime shifts)<\/strong>\u3002\u5982\u56fe3D\u6240\u793a\uff0c\u4e00\u4e9b\u7279\u6b8a\u7cfb\u7edf\u4e5f\u4f1a\u5728\u7279\u5b9a\u7684\u63a7\u5236\u53c2\u6570\u8303\u56f4\u5185\u4ea7\u751f\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001 <\/span>(alternative stable states) <\/span>\u6216\u591a\u7a33\u6001<\/span> (multiple stable states)<\/span>[27]\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u76f8\u53d8\u5728\u6240\u6709\u73af\u5883\u4e0b\u5747\u5448\u5355\u4e00\u72b6\u6001<\/span>\uff08\u5c3d\u7ba1\u72b6\u6001\u5728\u9608\u503c\u5904\u53ef\u80fd\u53d1\u751f\u53d8\u5316\uff09<\/span>\u3002\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u7684\u5b58\u5728\u610f\u5473\u7740\u5728\u76f8\u540c\u73af\u5883\u4e0b\uff0c\u81f3\u5c11\u5728\u4e00\u5b9a\u8303\u56f4\u5185\u53ef\u4ee5\u51fa\u73b0\u4e24\u79cd\u4e0d\u540c\u7684\u7a33\u6001\uff0c\u5176\u4e2d\u7ecf\u5e38\u51fa\u73b0\u6ede\u56de\u76f8\u53d8<\/span> (hysteresis phase transition)<\/span>\u3002\u5728\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u60c5\u51b5\u4e0b\uff0c\u72b6\u6001\u4e4b\u95f4\u7684\u8f6c\u53d8\u8868\u73b0\u4e3a\u5f3a\u70c8\u7684\u8d28\u53d8\uff0c\u76f8\u53d8\u60c5\u51b5\u5219\u8868\u73b0\u4e3a\u7b80\u5355\u7684\u91cf\u53d8\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe3. \u4e0d\u540c\u7c7b\u578b\u7684\u7cfb\u7edf\u72b6\u6001\u54cd\u5e94\u66f2\u7ebf\u3002(A)\u7cfb\u7edf\u7684\u72b6\u6001\u5bf9\u73af\u5883\u53d8\u5316\u505a\u51fa\u7ebf\u6027\u54cd\u5e94\uff1b(B)\u968f\u7740\u73af\u5883\u53c2\u6570\u7684\u589e\u52a0\uff0c\u4ece\u201c\u4e0a\u201d\u5230\u201c\u4e0b\u201d\u7684\u6301\u7eed\u72b6\u6001\u8f6c\u79fb\uff1b(C)\u4e24\u4e2a\u76f8\u4e92\u6392\u65a5\u7684\u7a33\u6001\u4e4b\u95f4\u53d1\u751f\u7a81\u7136\u7684\u72b6\u6001\u8f6c\u79fb\uff1b(D)\u6ede\u56de\u7cfb\u7edf\u4e2d\u5728\u591a\u4e2a\u5173\u952e\u9608\u503c\u5904\u53d1\u751f\u591a\u7a33\u6001\u95f4\u7684\u72b6\u6001\u8f6c\u79fb\u3002<\/span><\/p>\n


<\/h4>\n

\uff081\uff09\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001 (alternative stable states)\uff1a<\/span><\/strong><\/span><\/h4>\n

<\/span><\/section>\n
\u7cfb\u7edf\u4e2d\u7684\u4ea4\u66ff\u7a33\u5b9a\u53ef\u4ee5\u7528\u56fe4\u4e2d\u7684\u201c\u676f\u4e2d\u5c0f\u7403\u201d\u6765\u8868\u793a [28]\u3002\u82e5\u7528\u5c0f\u7403\u4f4d\u7f6e\u8868\u793a\u7cfb\u7edf\u7684\u5b9e\u9645\u72b6\u6001\uff0c\u5728\u6ca1\u6709\u5916\u754c\u5e72\u9884\u7684\u60c5\u51b5\u4e0b\uff0c\u5c0f\u7403\u603b\u4f1a\u5411\u7740\u66f4\u4f4e\u7684\u4f4d\u7f6e\u79fb\u52a8\uff0c\u5e76\u6700\u7ec8\u7a33\u5b9a\u5728\u67d0\u4e2a\u72b6\u6001\u4e2d\u3002\u90a3\u5982\u4f55\u5b9e\u73b0\u5c0f\u7403\u4ece\u4e00\u4e2a\u7a33\u5b9a\u72b6\u6001\u79fb\u52a8\u81f3\u53e6\u4e00\u4e2a\u7a33\u5b9a\u72b6\u6001\u5462\uff1f<\/span><\/span>\u65b9\u6cd5\u4e00\u662f\u6539\u53d8\u5c0f\u7403\u7684\u4f4d\u7f6e\uff08\u5982\u5de6\u56fe\uff09\uff0c\u5373\u5bf9\u672c\u8eab\u72b6\u6001\u53d8\u91cf\u8fdb\u884c\u5927\u89c4\u6a21\u6270\u52a8\u3002\u65b9\u6cd5\u4e8c\u662f\u6539\u53d8\u5c0f\u7403\u6240\u5c5e\u7684\u73af\u5883\uff08\u5982\u53f3\u56fe\uff09\uff0c\u5373\u6539\u53d8\u63a7\u5236\u52a8\u529b\u7cfb\u7edf\u5185\u90e8\u7684\u76f8\u4e92\u4f5c\u7528\u53c2\u6570\u3002<\/span><\/strong><\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n
\u56fe4. \u201c\u676f\u4e2d\u5c0f\u7403\u201d\u72b6\u6001\u8f6c\u79fb\u60c5\u51b5\u3002<\/span><\/section>\n


<\/h4>\n

\uff082\uff09\u7a81\u7136\u76f8\u53d8 (abrupt phase shifts) \u548c\u4e34\u754c\u70b9 (tipping points)<\/span><\/strong><\/span><\/h4>\n

<\/span><\/section>\n
\u5f53\u5916\u90e8\u73af\u5883\u6216\u63a7\u5236\u53c2\u6570\u8d85\u8fc7\u67d0\u4e00\u4e34\u754c\u70b9\u65f6\uff0c\u5f80\u5f80\u4f1a\u5e26\u6765\u707e\u96be\u6027\u4e14\u4e0d\u53ef\u9006\u7684\u540e\u679c\u3002\u56e0\u6b64\uff0c\u51c6\u786e\u9884\u6d4b\u7cfb\u7edf\u7684\u7a81\u7136\u76f8\u53d8\u548c\u4e34\u754c\u70b9\u662f\u7f51\u7edc\u97e7\u6027\u7684\u91cd\u8981\u4e3b\u9898\u4e4b\u4e00\u3002<\/strong>\u5177\u6709\u4ea4\u66ff\u7a33\u6001\u7684\u72b6\u6001\u7a81\u53d8\u901a\u5e38\u4e0e\u5206\u5c94<\/span> (bifurcation) <\/span>\u548c\u7a81\u53d8\u7406\u8bba<\/span>\uff08catastrophe theory\uff09<\/span>\u6709\u5173[29,30]\uff0c\u5982\u56fe3D\u6240\u793a\u3002\u7531\u4e8e\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\u5f88\u96be\u6536\u96c6\u5230\u5173\u4e8e\u5206\u5c94\u7684\u7ecf\u9a8c\u6570\u636e\uff0c\u4ece\u591a\u4e2a\u7a33\u5b9a\u72b6\u6001\u4e2d\u533a\u5206\u76f8\u53d8\u5b58\u5728\u96be\u5ea6\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u5c3d\u7ba1\u9700\u8981\u6709\u5305\u542b\u8bb8\u591a\u7a33\u6001\u8f6c\u79fb\u7684\u5927\u89c4\u6a21\u65f6\u95f4\u5e8f\u5217\uff0c\u4f46\u76ee\u524d\u5df2\u6709\u591a\u79cd\u65b9\u6cd5\u53ef\u4ee5\u7528\u6765\u63a8\u65ad\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u662f\u5426\u6d89\u53ca\u7a33\u6001\u8f6c\u79fb[31,32,33]\u3002<\/span><\/section>\n

<\/span><\/section>\n

\uff083\uff09\u4e34\u754c\u6162\u5316 (critical slowing down)<\/span><\/strong><\/span><\/h4>\n

<\/span><\/section>\n
\u5f53\u7cfb\u7edf\u63a5\u8fd1\u4f46\u6ca1\u6709\u8d8a\u8fc7\u4e34\u754c\u70b9\u65f6\uff0c\u53ef\u80fd\u4f1a\u53d1\u751f\u52a8\u529b\u5b66\u7cfb\u7edf\u7406\u8bba\u4e2d\u7684\u4e34\u754c\u6162\u5316\u73b0\u8c61[34]\u3002\u8be5\u73b0\u8c61\u8868\u73b0\u5728\u8d8a\u63a5\u8fd1\u4e34\u754c\u70b9\u65f6\uff0c\u7cfb\u7edf\u6062\u590d\u5230\u539f\u6709\u72b6\u6001\u7684\u901f\u7387\u4f1a\u53d8\u6162\u3001\u6301\u7eed\u65f6\u95f4\u53d8\u957f\u3001\u6062\u590d\u80fd\u529b\u53d8\u5f31<\/strong>\u3002\u56e0\u6b64\uff0c\u4e00\u4e2a\u5c0f\u6270\u52a8\u540e\u7684\u6062\u590d\u901f\u7387\u53ef\u4ee5\u7528\u6765\u8868\u660e\u7cfb\u7edf\u63a5\u8fd1\u5206\u5c94\u70b9\u7684\u7a0b\u5ea6\uff0c\u4e34\u754c\u6162\u5316\u73b0\u8c61\u4e5f\u88ab\u7528\u4f5c\u4e3a\u4e34\u754c\u70b9\u5230\u6765\u7684\u65e9\u671f\u9884\u8b66[35]\u3002\u901a\u8fc7\u7cfb\u7edf\u5730\u6d4b\u8bd5\u6062\u590d\u901f\u7387\u6765\u8bc4\u4f30\u4e34\u754c\u6162\u5316\u4e0d\u9002\u7528\u4e8e\u5927\u591a\u6570\u771f\u5b9e\u7cfb\u7edf\uff0c\u4f46\u51e0\u4e4e\u6240\u6709\u7684\u771f\u5b9e\u7cfb\u7edf\u90fd\u53d7\u5230\u6301\u7eed\u7684\u81ea\u7136\u6270\u52a8\u3002\u5f53\u63a5\u8fd1\u5206\u5c94\u65f6\uff0c\u4e34\u754c\u6162\u5316\u73b0\u8c61\u5728\u7cfb\u7edf\u52a8\u529b\u5b66\u4e2d\u5bfc\u81f4\u4e09\u79cd\u53ef\u80fd\u7684\u9884\u8b66\u4fe1\u53f7\uff1a\uff081\uff09\u4ece\u6270\u52a8\u4e2d\u6062\u590d\u901f\u7387\u8f83\u6162\uff1b\uff082\uff09\u81ea\u76f8\u5173\u6027\u589e\u52a0\uff08\u89c1\u56fe5\uff09\uff1b\uff083\uff09\u65b9\u5dee\u589e\u52a0[35]<\/strong>\u3002\u81ea\u76f8\u5173\u6027\u548c\u65b9\u5dee\u662f\u4e34\u754c\u6162\u5316\u7684\u95f4\u63a5\u5ea6\u91cf\uff0c\u5e76\u4e14\u4e24\u8005\u90fd\u9884\u8ba1\u5728\u4e34\u754c\u8f6c\u53d8\u4e4b\u524d\u589e\u52a0\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe5. \u5728\u65f6\u95f4\u5e8f\u5217\u4e2d\u4e34\u754c\u53d8\u5316\u7684\u65e9\u671f\u9884\u8b66\u4fe1\u53f7\u3002(A)\u751f\u7269\u91cf\u7684\u65f6\u95f4\u5e8f\u5217\uff1b(B)\u4e34\u754c\u53d8\u5316\u524d\u6ce2\u52a8\u7684\u632f\u5e45\u6709\u6240\u589e\u52a0\uff1b(C)\u65b9\u5dee\uff1b(D)AR(1)\u6a21\u578b\u53c2\u6570\u4f30\u8ba1\u3002<\/span><\/p>\n


<\/span><\/section>\n
\u7efc\u4e0a\u6240\u8ff0\uff0c\u590d\u6742\u7f51\u7edc\u901a\u5e38\u4ee5\u975e\u7ebf\u6027\u548c\u975e\u5355\u8c03\u7684\u65b9\u5f0f\u54cd\u5e94\u5916\u90e8\u6270\u52a8\u3002\u7531\u4e8e\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u7684\u5b58\u5728\uff0c\u5373\u4f7f\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\uff0c\u7f51\u7edc\u4e5f\u53ef\u80fd\u663e\u793a\u51fa\u5b8c\u5168\u4e0d\u540c\u7684\u72b6\u6001\uff0c\u8fd9\u4f7f\u5f97\u9884\u6d4b\u7a33\u6001\u8f6c\u79fb\u6216\u4e34\u754c\u70b9\u6781\u5177\u6311\u6218\u6027\u3002\u6bd4\u8f83\u5e78\u8fd0\u7684\u662f\uff0c\u5f53\u7cfb\u7edf\u63a5\u8fd1\u4e34\u754c\u70b9\u65f6\uff0c\u4e34\u754c\u6162\u5316\u73b0\u8c61\u53ca\u76f8\u5173\u6307\u6807\u80fd\u6709\u6548\u5730\u9884\u544a\u4e34\u754c\u70b9\u7684\u5230\u6765\u3002<\/span><\/section>\n

<\/span><\/section>\n

2.3 \u7f51\u7edc\u97e7\u6027\u5206\u6790\u5de5\u5177<\/span><\/strong><\/span><\/h3>\n

<\/span><\/section>\n
\u5728\u8fc7\u53bb\u768450\u5e74\u91cc\uff0c\u4eba\u4eec\u5f00\u53d1\u4e86\u8bb8\u591a\u5206\u6790\u5de5\u5177\u6765\u7814\u7a76\u4f4e\u7ef4\u7cfb\u7edf\u7684\u97e7\u6027\u73b0\u8c61\u6216\u9884\u6d4b\u4e34\u754c\u70b9\uff0c\u8fd9\u4e9b\u5de5\u5177\u5927\u591a\u81f4\u529b\u4e8e\u4f4e\u7ef4\u52a8\u529b\u5b66\u65b9\u7a0b\u7684\u5e73\u8861\u5206\u6790\u3002\u5bf9\u4e8e\u5927\u89c4\u6a21\u7f51\u7edc\uff0c\u9664\u4e86\u7f51\u7edc\u5185\u90e8\u52a8\u529b\u5b66\u53d8\u5316\u83ab\u6d4b\u4ee5\u5916\uff0c\u7f3a\u4e4f\u5408\u9002\u7684\u5206\u6790\u5de5\u5177\u4e5f\u5236\u7ea6\u7f51\u7edc\u97e7\u6027\u51c6\u786e\u9884\u6d4b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5bf9\u4e8e\u5b8c\u6574\u7f51\u7edc\uff0cGao\u7b49\u4eba[36]\u6700\u8fd1\u63d0\u51fa\u4e00\u4e2a\u80fd\u5c06\u9ad8\u7ef4\u7cfb\u7edf\u52a8\u529b\u5b66\u6620\u5c04\u4e3a\u6709\u6548\u7684\u4e00\u7ef4\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u901a\u7528\u6846\u67b6\uff0c\u79f0\u4e3aGBB\u964d\u7ef4\u7406\u8bba (GBB reduction theory)<\/strong>\u3002\u8be5\u6a21\u578b\u4e0d\u4ec5\u80fd\u51c6\u786e\u9884\u6d4b\u7cfb\u7edf\u5bf9\u5404\u79cd\u6270\u52a8\u7684\u54cd\u5e94\uff0c\u8fd8\u80fd\u51c6\u786e\u5b9a\u4f4d\u7cfb\u7edf\u5931\u53bb\u97e7\u6027\u7684\u4e34\u754c\u70b9\u3002\u8fd9\u9879\u5173\u4e8e\u590d\u6742\u7f51\u7edc\u666e\u904d\u97e7\u6027\u6a21\u5f0f\u7684\u7814\u7a76\u63d0\u51fa\u4e86\u53ef\u80fd\u7528\u4e8e\u907f\u514d\u97e7\u6027\u5931\u6548\u7684\u6f5c\u5728\u5e72\u9884\u7b56\u7565\uff0c\u4ee5\u53ca\u80fd\u6210\u529f\u5e94\u5bf9\u6270\u52a8\u7684\u6700\u4f73\u97e7\u6027\u7cfb\u7edf\u539f\u5219\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe6. \u591a\u7ef4\u7cfb\u7edf\u4e2d\u7684\u7f51\u7edc\u97e7\u6027\u3002(A)-(C)\u4e2d\u4e09\u7ef4\u56fe\u663e\u793a\u4e86\u56db\u4e2a\u8282\u70b9\u7cfb\u7edf\u7684\u97e7\u6027\u5e73\u9762\uff1b(D)\u91c7\u7528[36]\u4e2dGBB\u7406\u8bba\u540e\uff0c(A)-(C)\u4e2d\u7684\u591a\u7ef4\u6d41\u5f62\u964d\u7ef4\u6210\u4e00\u7ef4\u97e7\u6027\u51fd\u6570\u3002\u7814\u7a76\u8868\u660e\uff0c\u901a\u8fc7\u5c06\u591a\u7ef4\u7cfb\u7edf\u6620\u5c04\u5230\u03b2\u7a7a\u95f4\uff0c\u53ef\u4ee5\u51c6\u786e\u9884\u6d4b\u7cfb\u7edf\u7684\u5404\u79cd\u6270\u52a8\u548c\u4e34\u754c\u70b9\u3002<\/span><\/p>\n


<\/span><\/section>\n
\u6b64\u5916\uff0c\u5982\u4f55\u63a8\u65ad\u4e0d\u5b8c\u6574\u7f51\u7edc\u7684\u97e7\u6027\u4e5f\u662f\u4e00\u4e2a\u91cd\u8981\u95ee\u9898<\/span><\/strong>\u3002Jiang\u7b49\u4eba[37]\u5229\u7528\u964d\u7ef4\u4e2d\u7684\u5e73\u5747\u573a\u65b9\u6cd5\u6765\u5b66\u4e60\u7f51\u7edc\u4e2d\u90e8\u5206\u771f\u5b9e\u7a33\u5b9a\u72b6\u6001\uff0c\u800c\u4e0d\u9700\u8981\u77e5\u9053\u6574\u4e2a\u7f51\u7edc\u4fe1\u606f\u3002\u5927\u591a\u6570\u771f\u5b9e\u7f51\u7edc<\/span>\uff08\u4e3b\u8981\u662f\u751f\u7269\u548c\u751f\u6001\u7f51\u7edc\uff09<\/span>\u662f\u4e0d\u5b8c\u6574\u7684\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u8f85\u52a9\u63a8\u65ad\u7f51\u7edc\u771f\u5b9e\u7684\u52a8\u529b\u5b66\u7279\u5f81\u3002\u540c\u6837\uff0cJiang\u7b49\u4eba[38]\u5c06\u5e73\u5747\u573a\u7406\u8bba\u548c\u7ec4\u5408\u4f18\u5316\u76f8\u7ed3\u5408\uff0c\u4ece\u89c2\u5bdf\u5230\u7684\u4e0d\u5b8c\u6574\u7f51\u7edc\u4e2d\u63a8\u65ad\u51fa\u62d3\u6251\u5b66\u7279\u5f81\uff0c\u5982\u5ea6\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

\u56fe7. \u57fa\u4e8e5\u4e2a\u7269\u79cd\u7684\u76f8\u4e92\u4f5c\u7528\u5173\u7cfb\uff0c\u9884\u6d4b\u5305\u542b97\u4e2a\u7269\u79cd\u7684\u751f\u6001\u7f51\u7edc\u7a33\u6001\u4e30\u5ea6[37]\u3002<\/span><\/p>\n


<\/section>\n
\u9664\u4e86\u7f51\u7edc\u5c42\u9762\u7684\u97e7\u6027\u73b0\u8c61\u4e4b\u5916\uff0c\u6bcf\u4e2a\u8282\u70b9\u5bf9\u4e8e\u7f51\u7edc\u97e7\u6027\u7684\u8d21\u732e\u53c8\u5982\u4f55\u5462\uff1f<\/span><\/strong>\u57fa\u4e8e\u7b49\u4ef7\u7684\u4e00\u7ef4\u6a21\u578b\uff0cZhang\u7b49\u4eba[39]\u63d0\u51fa\u201c\u97e7\u6027\u4e2d\u5fc3\u6027\u201d<\/span> (resilience centrality) <\/span>\u6765\u91cf\u5316\u8282\u70b9\u5bf9\u7cfb\u7edf\u97e7\u6027\u7684\u5f71\u54cd\u80fd\u529b\u3002\u97e7\u6027\u4e2d\u5fc3\u6027\u4e3b\u8981\u7531\u8282\u70b9\u7684\u5ea6\u548c\u52a0\u6743\u6700\u8fd1\u90bb\u5ea6\u51b3\u5b9a\uff0c\u8be5\u6307\u6807\u80fd\u5e2e\u52a9\u4eba\u4eec\u8bbe\u8ba1\u51fa\u6709\u6548\u7684\u771f\u5b9e\u7f51\u7edc\u4fdd\u62a4\u7b56\u7565<\/span>\uff08\u5982\u4e92\u60e0\u7f51\u7edc\u548c\u57fa\u7840\u8bbe\u65bd\u7cfb\u7edf\uff09<\/span>\u3002<\/span><\/section>\n


<\/span><\/h3>\n

2.4 \u4e09\u4e2a\u76f8\u4f3c\u6982\u5ff5\u8fa8\u6790<\/span><\/strong><\/span><\/span><\/h3>\n

<\/section>\n
\u7a33\u5b9a\u6027<\/span><\/strong> (stability) <\/span>\u548c\u9c81\u68d2\u6027<\/strong><\/span> (robustness) <\/span>\u90fd\u4e0e\u97e7\u6027<\/strong>\u5bc6\u5207\u76f8\u5173\uff0c\u5b83\u4eec\u901a\u5e38\u7528\u4e8e\u5206\u6790\u7cfb\u7edf\u5728\u4e0d\u65ad\u53d8\u5316\u7684\u6761\u4ef6\u4e0b\u5982\u4f55\u54cd\u5e94\uff0c\u6709\u65f6\u5f88\u96be\u533a\u5206[40]\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u97e7\u6027\u662f\u7cfb\u7edf\u7684\u6301\u4e45\u6027\u5c5e\u6027\uff0c\u7a33\u5b9a\u6027\u8868\u793a\u4e00\u4e2a\u7cfb\u7edf\u5728\u53d7\u5230\u4e34\u65f6\u6270\u52a8\u540e\u8fd4\u56de\u5230\u4e00\u4e2a\u7279\u5b9a\u7a33\u6001\u7684\u80fd\u529b<\/strong>\uff0c\u8fd9\u4e24\u4e2a\u6982\u5ff5\u90fd\u662f\u5728\u7f51\u7edc\u52a8\u529b\u5b66\u7684\u80cc\u666f\u4e0b\u5b9a\u4e49\u7684[36,3]\u3002\u9c81\u68d2\u6027\u7684\u6982\u5ff5\u901a\u5e38\u4e0e\u7f51\u7edc\u9759\u6001\u7ed3\u6784\u6709\u5173<\/strong>\uff0c\u5b83\u8861\u91cf\u7684\u662f\u5f53\u7f51\u7edc\u7684\u4e00\u90e8\u5206\u8282\u70b9\u6216\u8fb9\u5931\u6548\u65f6\uff0c\u7f51\u7edc\u7ef4\u6301\u8fde\u901a\u7684\u80fd\u529b[41]\u3002<\/span><\/section>\n

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\u27a2 \u7a33\u5b9a\u6027\uff1astability\u4e00\u8bcd\u6765\u81ea\u62c9\u4e01\u8bedstabilis\uff0c\u610f\u4e3a\u575a\u5b9a\u6216\u7262\u9760\u3002\u7a33\u5b9a\u6027\u4e3b\u8981\u5e94\u7528\u4e8e\u751f\u6001\u5b66\u4e2d[46]\uff0c\u8868\u793a\u53d7\u5230\u6270\u52a8\u7684\u60c5\u51b5\u4e0b\u7cfb\u7edf\u4fdd\u6301\u751f\u6001\u529f\u80fd\u548c\u6062\u590d\u5230\u521d\u59cb\u5e73\u8861\u72b6\u6001\u7684\u80fd\u529b[43]\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5177\u6709\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u7684\u7cfb\u7edf\uff0c\u7a33\u5b9a\u6027\u53d6\u51b3\u4e8e\u4ea4\u66ff\u7a33\u5b9a\u72b6\u6001\u7684\u6570\u91cf\u2014\u2014\u53ef\u80fd\u7684\u7a33\u5b9a\u72b6\u6001\u8d8a\u5c11\uff0c\u7cfb\u7edf\u8d8a\u7a33\u5b9a\u3002\u201c\u97e7\u6027\u201d\u96c6\u4e2d\u5728\u5438\u5f15\u57df\u7684\u8fb9\u754c\u4e0a\uff0c\u800c “\u7a33\u5b9a\u6027 “\u5219\u96c6\u4e2d\u5728\u5e73\u8861\u72b6\u6001\u4e0a\u3002\u4e00\u65b9\u9762\uff0c\u4e00\u4e2a\u7cfb\u7edf\u53ef\u4ee5\u662f\u975e\u5e38\u6709\u97e7\u6027\u7684\uff0c\u4f46\u5b58\u5728\u6709\u5f88\u5927\u7684\u6ce2\u52a8\uff0c\u5373\u7a33\u5b9a\u6027\u4f4e\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4e00\u4e2a\u7a33\u5b9a\u7684\u7cfb\u7edf\u53ef\u80fd\u5177\u6709\u4f4e\u97e7\u6027\u3002<\/span><\/section>\n

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\u27a2 \u9c81\u68d2\u6027\uff1arobustness\u6765\u6e90\u4e8e\u62c9\u4e01\u8bed quercus robur\uff0c\u5728\u53e4\u4ee3\u4e16\u754c\u662f\u529b\u91cf\u4e0e\u957f\u5bff\u7684\u8c61\u5f81\u3002\u4e00\u4e2a\u7cfb\u7edf\u7684\u9c81\u68d2\u6027\u662f\u6307\u7cfb\u7edf\u5728\u4e0d\u4e27\u5931\u529f\u80fd\u7684\u60c5\u51b5\u4e0b\u627f\u53d7\u6545\u969c\u548c\u6270\u52a8\u7684\u80fd\u529b\u3002\u4f8b\u5982\uff0c\u751f\u7269\u5b66\u5bb6\u5c06\u9c81\u68d2\u6027\u5b9a\u4e49\u4e3a\u751f\u7269\u7cfb\u7edf\u5728\u4e0d\u53ef\u9884\u6d4b\u7684\u6270\u52a8\u4e0b\u4ecd\u80fd\u4fdd\u6301\u7279\u5b9a\u529f\u80fd\u7684\u80fd\u529b[44]\uff1b\u5728\u7f51\u7edc\u79d1\u5b66\u4e2d\uff0c\u9c81\u68d2\u6027\u8861\u91cf\u5176\u5728\u4e00\u90e8\u5206\u8282\u70b9\u6216\u8fb9\u88ab\u7834\u574f\u65f6\u4fdd\u6301\u8fde\u63a5\u7684\u80fd\u529b[45] \uff1b\u5728\u6570\u5b66\u4e0a\uff0c\u7f51\u7edc\u7684\u9c81\u68d2\u6027\u88ab\u5efa\u6a21\u4e3a\u4e00\u4e2a\u53cd\u5411\u6e17\u6d41\u8fc7\u7a0b[46]\u3002<\/span><\/section>\n

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\u56fe8. \u7f51\u7edc\u9c81\u68d2\u6027\u53ef\u7406\u89e3\u4e3a\u968f\u673a\u79fb\u9664\u90e8\u5206\u8282\u70b9\u540e\u5de8\u7247\u7684\u5927\u5c0f[47]\u3002<\/span><\/section>\n


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\u97e7\u6027\u662f\u63cf\u8ff0\u7cfb\u7edf\u53d7\u5230\u6270\u52a8\u5e76\u7ef4\u6301\u5176\u57fa\u672c\u529f\u80fd\u7684\u80fd\u529b\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u751f\u7269\u3001\u793e\u4f1a\u3001\u5de5\u7a0b\u7b49\u591a\u4e2a\u5b66\u79d1\u9886\u57df\u3002\u8be5\u7efc\u8ff0\u4ecb\u7ecd\u4e86\u4f4e\u7ef4\u7cfb\u7edf\u97e7\u6027\u5230\u591a\u7ef4\u7f51\u7edc\u97e7\u6027\u7684\u6f14\u53d8\uff0c\u5e76\u57fa\u4e8e\u5927\u89c4\u6a21\u7f51\u7edc\u7684\u7406\u8bba\u5de5\u5177\u548c\u5148\u8fdb\u7684\u6570\u636e\u5206\u6790\u6280\u672f\uff0c\u91cd\u70b9\u63a2\u8ba8\u4e86\u5982\u76f8\u53d8<\/span> (phase shift)<\/span>\u3001\u7a33\u6001\u8f6c\u53d8<\/span>(regime shifts)<\/span>\u7b49\u4fbf\u4e8e\u7406\u89e3\u7f51\u7edc\u97e7\u6027\u7684\u6838\u5fc3\u4e3b\u9898\u3002\u540c\u65f6\uff0c\u6587\u7ae0\u8fa8\u6790\u4e86\u7cfb\u7edf\u201c\u7a33\u5b9a\u6027\u201d\u3001\u201c\u9c81\u68d2\u6027\u201d\u548c\u201c\u97e7\u6027\u201d\u4e09\u4e2a\u5e38\u89c1\u5c5e\u6027\u7684\u533a\u522b\u4e0e\u5173\u8054\uff0c\u6709\u5229\u4e8e\u8fdb\u4e00\u6b65\u52a0\u6df1\u5bf9\u7f51\u7edc\u97e7\u6027\u53ca\u5176\u52a8\u529b\u5b66\u7684\u7406\u89e3\u3002<\/span><\/section>\n

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[1] Giliberto Capano, Jun Jie Woo, Resilience and robustness in policy design: A critical appraisal, Policy Sci. 50 (3) (2017) 399\u2013426.<\/span><\/section>\n
[2] Len Fisher, More than 70 ways to show resilience, Nature 518 (7537) (2015) 35.<\/span><\/section>\n
[3] Crawford S. Holling, Resilience and stability of ecological systems, Annu. Rev. Ecol. Syst. 4 (1) (1973) 1\u201323.<\/span><\/section>\n
[4] Crawford Stanley Holling, Engineering resilience versus ecological resilience, Eng. Within Ecol. Constr. 31 (1996) (1996) 32.<\/span><\/section>\n
[5]Lei Dai, Kirill S. Korolev, Jeff Gore, Slower recovery in space before collapse of connected populations, Nature 496 (7445) (2013) 355.<\/span><\/section>\n
[6]Marten Scheffer, Steve Carpenter, Jonathan A. Foley, Carl Folke, Brian Walker, Catastrophic shifts in ecosystems, Nature 413 (6856) (2001) 591.<\/span><\/section>\n
[7] Marten Scheffer, Jordi Bascompte, William A. Brock, Victor Brovkin, Stephen R. Carpenter, Vasilis Dakos, Hermann Held, Egbert H. Van Nes, Max Rietkerk, George Sugihara, Early-warning signals for critical transitions, Nature 461 (7260) (2009) 53.<\/span><\/section>\n
[8] Albert-L\u00e1szl\u00f3 Barab\u00e1si, R\u00e9ka Albert, Emergence of scaling in random networks, Science 286 (5439) (1999) 509\u2013512.<\/span><\/section>\n
[9] Wen-Xu Wang, Ying-Cheng Lai, Celso Grebogi, Data based identification and prediction of nonlinear and complex dynamical systems, Phys. Rep. 644 (2016) 1\u201376.<\/span><\/section>\n
[10] Baruch Barzel, Yang-Yu Liu, Albert-L\u00e1szl\u00f3 Barab\u00e1si, Constructing minimal models for complex system dynamics, Nature Commun. 6 (2015) 7186.<\/span><\/section>\n
[11] Crawford S. Holling, Resilience and stability of ecological systems, Annu. Rev. Ecol. Syst. 4 (1) (1973) 1\u201323.<\/span><\/section>\n
[12] Hannah R. Meredith, Virgile Andreani, Helena R. Ma, Allison J. Lopatkin, Anna J. Lee, Deverick J. Anderson, Gregory Batt, Lingchong You, Applying ecological resistance and resilience to dissect bacterial antibiotic responses, Sci. Adv. 4 (12) (2018) eaau1873.<\/span><\/section>\n
[13] Talcott Parsons, Edward A. Shils, Neil J. Smelser, The social system, in: Toward a General Theory of Action, Routledge, 2017, pp. 190\u2013233.<\/span><\/section>\n
[14] Erik Hollnagel, David D. Woods, Nancy Leveson, Resilience Engineering: Concepts and Precepts, Ashgate Publishing, Ltd., 2006.<\/span><\/section>\n
[15] Rachel J. Standish, Richard J. Hobbs, Margaret M. Mayfield, Brandon T. Bestelmeyer, Katherine N. Suding, Loretta L. Battaglia, Valerie Eviner, Christine V. Hawkes, Vicky M. Temperton, Viki A. Cramer, et al., Resilience in ecology: Abstraction, distraction, or where the action is? Biol. Cons. 177 (2014) 43\u201351.<\/span><\/section>\n
[16] Igor Volkov, Jayanth R. Banavar, Stephen P. Hubbell, Amos Maritan, Neutral theory and relative species abundance in ecology, Nature 424 (6952) (2003) 1035.<\/span><\/section>\n
[17] Maksim Kitsak, Lazaros K. Gallos, Shlomo Havlin, Fredrik Liljeros, Lev Muchnik, H. Eugene Stanley, Hern\u00e1n A. Makse, Identification of influential spreaders in complex networks, Nat. Phys. 6 (11) (2010) 888.<\/span><\/section>\n
[18] Mark E.J. Newman, The structure and function of complex networks, SIAM Rev. 45 (2) (2003) 167\u2013256.<\/span><\/section>\n
[19] Liming Pan, Dan Yang, Wei Wang, Shimin Cai, Tao Zhou, Ying-Cheng Lai, Phase diagrams of interacting spreading dynamics in complex networks, Phys. Rev. Res. 2 (2) (2020) 023233.<\/span><\/section>\n
[20] Huanfei Ma, Siyang Leng, Kazuyuki Aihara, Wei Lin, Luonan Chen, Randomly distributed embedding making short-term high-dimensional data predictable, Proc. Natl. Acad. Sci. 115 (43) (2018) E9994\u2013E10002.<\/span><\/section>\n
[21] Gouhei Tanaka, Kai Morino, Kazuyuki Aihara, Dynamical robustness of complex biological networks, in: Mathematical Approaches to Biological<\/span><\/section>\n
Systems, Springer, 2015, pp. 29\u201353.<\/span><\/section>\n
[22] Uri Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, CRC Press, 2006.<\/span><\/section>\n
[23] Marian Bogun\u00e1, Claudio Castellano, Romualdo Pastor-Satorras, Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks, Phys. Rev. Lett. 111 (6) (2013) 068701.<\/span><\/section>\n
[24] David Tilman, Joseph Fargione, Brian Wolff, Carla D\u2019antonio, Andrew Dobson, Robert Howarth, David Schindler, William H. Schlesinger, Daniel Simberloff, Deborah Swackhamer, Forecasting agriculturally driven global environmental change, Science 292 (5515) (2001) 281\u2013284.<\/span><\/section>\n
[25] Peter J. Mumby, Robert S. Steneck, Alan Hastings, Evidence for and against the existence of alternate attractors on coral reefs, Oikos 122 (4) (2013) 481\u2013491.<\/span><\/section>\n
[26] Steve R. Dudgeon, Richard B. Aronson, John F. Bruno, William F. Precht, Phase shifts and stable states on coral reefs, Mar. Ecol. Prog. Ser. 413 (2010) 201\u2013216.<\/span><\/section>\n
[27] Marten Scheffer, Steve Carpenter, Jonathan A. Foley, Carl Folke, Brian Walker, Catastrophic shifts in ecosystems, Nature 413 (6856) (2001) 591.<\/span><\/section>\n
[28] Beatrix E. Beisner, Daniel T. Haydon, Kim Cuddington, Alternative stable states in ecology, Front. Ecol. Environ. 1 (7) (2003) 376\u2013382.<\/span><\/section>\n
[29] Michael G. Crandall, Paul H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (2) (1971) 321\u2013340.<\/span><\/section>\n
[30] Erik Christopher Zeeman, Catastrophe theory, in: Structural Stability in Physics, Springer, 1979, pp. 12\u201322.<\/span><\/section>\n
[31] Stephen R. Carpenter, Alternate states of ecosystems: evidence and some implications, Ecol. Achiev. Challenge (2001) 357\u2013383.<\/span><\/section>\n
[32] William A. Broock, Jos\u00e9 Alexandre Scheinkman, W. Davis Dechert, Blake LeBaron, A test for independence based on the correlation dimension, Econometric Rev. 15 (3) (1996) 197\u2013235.<\/span><\/section>\n
[33] Stephen R. Carpenter, Michael L. Pace, Dystrophy and eutrophy in lake ecosystems: implications of fluctuating inputs, Oikos (1997) 3\u201314.<\/span><\/section>\n
[34] C. Wissel, A universal law of the characteristic return time near thresholds, Oecologia 65 (1) (1984) 101\u2013107.<\/span><\/section>\n
[35] Marten Scheffer, Jordi Bascompte, William A. Brock, Victor Brovkin, Stephen R. Carpenter, Vasilis Dakos, Hermann Held, Egbert H. Van Nes, Max Rietkerk, George Sugihara, Early-warning signals for critical transitions, Nature 461 (7260) (2009) 53.<\/span><\/section>\n
[36] Jianxi Gao, Baruch Barzel, Albert-L\u00e1szl\u00f3 Barab\u00e1si, Universal resilience patterns in complex networks, Nature 530 (7590) (2016) 307.<\/span><\/section>\n
[37] Chunheng Jiang, Jianxi Gao, Malik Magdon-Ismail, True nonlinear dynamics from incomplete networks, in: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, (01) 2020, pp. 131\u2013138.<\/span><\/section>\n
[38] Chunheng Jiang, Jianxi Gao, Malik Magdon-Ismail, Inferring degrees from incomplete networks and nonlinear dynamics, in: Christian Bessiere(Ed.), Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI-20, International Joint Conferences on Artificial Intelligence Organization, 2020, pp. 3307\u20133313, Main track.<\/span><\/section>\n
[39] Yongtao Zhang, Cunqi Shao, Shibo He, Jianxi Gao, Resilience centrality in complex networks, Phys. Rev. E 101 (2) (2020) 022304.<\/span><\/section>\n
[40] Nicolas Urruty, Delphine Tailliez-Lefebvre, Christian Huyghe, Stability, robustness, vulnerability and resilience of agricultural systems. a review, Agron. Sustain. Dev. 36 (1) (2016) 15.<\/span><\/section>\n
[41] R\u00e9ka Albert, Hawoong Jeong, Albert-L\u00e1szl\u00f3 Barab\u00e1si, Error and attack tolerance of complex networks, Nature 406 (6794) (2000) 378\u2013382.<\/span><\/section>\n
[42] Anthony R. Ives, Stephen R. Carpenter, Stability and diversity of ecosystems, Science 317 (5834) (2007) 58\u201362.<\/span><\/section>\n
[43] Monica G. Turner, William H. Romme, Robert H. Gardner, Robert V. O\u2019Neill, Timothy K. Kratz, A revised concept of landscape equilibrium: disturbance and stability on scaled landscapes, Landscape Ecol. 8 (3) (1993) 213\u2013227.<\/span><\/section>\n
[44] Hiroaki Kitano, Biological robustness, Nature Rev. Genet. 5 (11) (2004) 826\u2013837.<\/span><\/section>\n
[45] Xueming Liu, Hao Peng, Jianxi Gao, Vulnerability and controllability of networks of networks, Chaos Solitons Fractals 80 (2015) 125\u2013138.<\/span><\/section>\n
[46] Sergey V. Buldyrev, Roni Parshani, Gerald Paul, H. Eugene Stanley, Shlomo Havlin, Catastrophic cascade of failures in interdependent networks, Nature 464 (7291) (2010) 1025.<\/span><\/section>\n
[47] Albert-L\u00e1szl\u00f3 Barab\u00e1si, et al., Network Science, Cambridge University Press, 2016.<\/span><\/section>\n


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