{"id":45072,"date":"2023-09-12T21:01:04","date_gmt":"2023-09-12T13:01:04","guid":{"rendered":"https:\/\/swarma.org\/?p=45072"},"modified":"2023-09-12T21:01:04","modified_gmt":"2023-09-12T13:01:04","slug":"nature-physics%e7%bb%bc%e8%bf%b0%ef%bc%9a%e5%a4%9a%e8%80%85%e5%bc%82%e4%b9%9f%e5%9c%a8%e7%9c%9f%e5%ae%9e%e4%b8%96%e7%95%8c%e5%a4%9a%e5%b1%82%e7%bd%91%e7%bb%9c%e4%b8%ad%e5%a6%82","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=45072","title":{"rendered":"Nature Physics\u7efc\u8ff0\uff1a\u201c\u591a\u8005\u5f02\u4e5f\u201d\u5728\u771f\u5b9e\u4e16\u754c\u591a\u5c42\u7f51\u7edc\u4e2d\u5982\u4f55\u4f53\u73b0\uff1f"},"content":{"rendered":"
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De Domenico \u6709\u4e00\u4e2a\u540d\u4e3a\u201cComplexity Thoughts\u201d\u7684\u535a\u5ba2\uff0c\u4ecb\u7ecd\u5173\u4e8e\u590d\u6742\u7cfb\u7edf\u7684\u6700\u65b0\u601d\u8003\uff1ahttps:\/\/manlius.substack.com\/\uff0c\u6211\u4eec\u4f1a\u5728\u4e4b\u540e\u9646\u7eed\u4ecb\u7ecd\u7ed9\u5927\u5bb6 \ud83d\ude0a<\/span><\/section>\n
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\u591a\u5c42\u7f51\u7edc<\/span><\/strong>\uff08multilayer network\uff0c\u53c8\u79f0\u7f51\u7edc\u7684\u7f51\u7edc Network of network, NoN\uff09<\/span>\u4e2d\uff0c\u540c\u4e00\u8282\u70b9\u53ef\u4ee5\u5b58\u5728\u4e8e\u4e00\u4e2a\u6216\u591a\u4e2a\u5c42\u4e2d\u3002\u5176\u4e2d\u72b6\u6001\u8282\u70b9<\/span>\uff08state node\uff09<\/span>\u662f\u9488\u5bf9\u7279\u5b9a\u5c42\u7684\u8282\u70b9\uff0c\u800c\u7269\u7406\u8282\u70b9<\/span>\uff08physical node\uff09<\/span>\u5219\u662f\u65e0\u8bba\u54ea\u4e00\u5c42\u7684\u8282\u70b9\u3002\u540c\u4e00\u7269\u7406\u8282\u70b9\u7684\u72b6\u6001\u8282\u70b9\u901a\u5e38\u88ab\u79f0\u4e3a\u526f\u672c<\/span>\uff08replica\uff09<\/span>\u3002\u72b6\u6001\u8282\u70b9\u901a\u8fc7\u5c42\u5185<\/span>\uff08\u5728\u540c\u4e00\u5c42\u5185\uff09<\/span>\u6216\u5c42\u95f4<\/span>\uff08\u8de8\u4e0d\u540c\u5c42\uff09<\/span>\u7684\u8fb9\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u4e9b\u8fb9\u53ef\u4ee5\u662f\u6709\u5411\u7684\u6216\u65e0\u5411\u7684\u3002<\/span><\/section>\n
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\u975e\u76f8\u4e92\u8fde\u63a5\u7684\u591a\u5c42\u7f51\u7edc<\/span><\/strong>\uff08non-interconnected multiplexes\uff0c\u56fe1\u5de6\uff09<\/span>\u4e2d\uff0c\u72b6\u6001\u8282\u70b9\u4e0d\u901a\u8fc7\u4e0d\u540c\u5c42\u4e4b\u95f4\u7684\u8fb9\u76f8\u4e92\u8fde\u63a5\u3002\u5728\u8fd9\u7c7b\u7cfb\u7edf\u4e2d\uff0c\u8de8\u8d8a\u5c42\u7ea7\u7684\u4fe1\u606f\u53ef\u4ee5\u5b9e\u65f6\u4e14\u65e0\u6210\u672c\u5730\u4ece\u4e00\u4e2a\u72b6\u6001\u8282\u70b9\u4f20\u9012\u5230\u5176\u526f\u672c\u3002\u56fe1\u6700\u53f3\u8fb9\u4e3a\u975e\u76f8\u4e92\u8fde\u63a5\u7684\u7f51\u7edc\uff0c\u4f8b\u5982\u6bcf\u4e00\u5c42\u4ee3\u8868\u4e0d\u540c\u7684\u793e\u4ea4\u7f51\u7edc\u5e73\u53f0\uff0c\u5176\u4e2d\u7684\u8282\u70b9\u4ee3\u8868\u540c\u65f6\u4f7f\u7528\u4e09\u4e2a\u5e73\u53f0\u7684\u7528\u6237\uff0c\u7528\u6237\u4f1a\u5728\u77ac\u95f4\u8fdb\u884c\u4fe1\u606f\u6c9f\u901a\uff0c\u4f8b\u5982\u5728\u5e73\u53f0A\u83b7\u5f97\u4e86\u67d0\u4e00\u6d88\u606f\uff0c\u5b9e\u65f6\u5f71\u54cd\u5176\u5728\u5176\u5b83\u5e73\u53f0\u7684\u884c\u4e3a\u3002\u5176\u4e2d\u7eff\u8272\u7684\u5c42\u4ee3\u8868\u8282\u70b9\u72b6\u6001\uff0c\u9ec4\u8272\u4e0e\u7ea2\u8272\u7684\u5c42\u4ee3\u8868\u4e0d\u540c\u7f51\u7edc\u5bf9\u5e94\u7684\u7269\u7406\u5b9e\u4f53\uff0c\u56fe\u4e2d\u7684\u7269\u7406\u8fde\u63a5\u8868\u793a\u6807\u51fa\u7684\u8282\u70b9\u4e3a\u540c\u4e00\u7269\u7406\u5b9e\u4f53\u3002<\/span><\/section>\n
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\u76f8\u4e92\u8fde\u63a5\u7684\u591a\u5c42\u7f51\u7edc<\/span><\/strong>\u4e2d<\/span>\uff08\u56fe1\u4e2d\uff09<\/span>\uff0c\u72b6\u6001\u8282\u70b9\u901a\u8fc7\u4e0d\u540c\u5c42\u4e4b\u95f4\u7684\u8fb9\u76f8\u4e92\u8fde\u63a5\uff0c\u7f16\u7801\u4e86\u5728\u526f\u672c\u4e4b\u95f4\u4ea4\u6362\u4fe1\u606f\u7684\u6210\u672c\u3002\u8fd9\u91cc\u81f3\u5c11\u6709\u4e24\u7c7b\u591a\u5c42\u7f51\u7edc\uff1a\uff081\uff09\u4e92\u8fde\u7684\u591a\u5c42\u7f51\u7edc<\/span>\uff08interconnected multiplexes\uff09<\/span>\uff0c\u5176\u4e2d\u5404\u5c42\u7684\u8282\u70b9\u662f\u540c\u8d28\u7684<\/span>\uff08\u4f8b\u5982\uff0c\u6240\u6709\u8282\u70b9\u90fd\u662f\u7535\u7ad9\uff09<\/span>\uff0c\u4ee5\u53ca\uff082\uff09\u76f8\u4e92\u4f9d\u8d56\u7684\u7f51\u7edc<\/span>\uff08interdependent network\uff09<\/span>\uff0c\u5176\u4e2d\u5404\u5c42\u7684\u8282\u70b9\u662f\u5f02\u8d28\u7684<\/span>\uff08\u4f8b\u5982\uff0c\u4e00\u5c42\u7684\u8282\u70b9\u662f\u7535\u7ad9\uff0c\u53e6\u4e00\u5c42\u7684\u8282\u70b9\u662f\u81ea\u6cbb\u7cfb\u7edf\u7b49\uff09<\/span>\u3002<\/span><\/section>\n
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\u5bf9\u4e8e\u4e0d\u540c\u5c42\u7684\u8282\u70b9\u662f\u5f02\u8d28\u7684\u60c5\u51b5\uff0c\u4f8b\u5982\u56fe1\u4e2d\u95f4\u4e3a\u76f8\u4e92\u8fde\u63a5\u7684\u7f51\u7edc\uff0c\u6807\u9ec4\u7684\u5c42\u4e2d\u7684\u8282\u70b9\u662f\u4f9b\u7535\u7ad9\uff0c\u6807\u7ea2\u7684\u4e3a\u901a\u8baf\u57fa\u7ad9\u3002\u5982\u5c42\u95f4\u7684\u8fb9\u4ee3\u8868\u79bb\u6563\u4fe1\u606f\uff0c\u5219\u4e3a\u65e0\u5411\u8fb9\uff1b\u5982\u4e3a\u65f6\u5e8f\u7684\uff0c\u5219\u53ef\u901a\u8fc7\u6709\u5411\u8fb9\uff0c\u5c06\u4e0d\u540c\u65f6\u95f4\u70b9\u7684\u7f51\u7edc\u5f53\u4f5c\u4e0d\u540c\u5c42\uff0c\u6b64\u65b9\u6cd5\u53ef\u7528\u4e8e\u7814\u7a76\u75be\u75c5\u6216\u4fe1\u606f\u4f20\u64ad\u8fc7\u7a0b\uff0c\u63a8\u5bfc\u5f15\u8d77\u4f20\u64ad\u7206\u53d1\u7684\u4e34\u754c\u5bc6\u5ea6\u3002\u5982\u5c42\u95f4\u5b58\u5728\u76f8\u4e92\u4f5c\u7528\uff0c\u5219\u53ef\u4f7f\u7528\u53cc\u5411\u8fde\u8fb9\u3002<\/span><\/section>\n
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3. \u591a\u5c42\u7f51\u7edc\u5efa\u6a21\u7684\u6311\u6218<\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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\u4e00\u822c\u7684\u591a\u5c42\u7f51\u7edc\u5982\u91c7\u53d6\u7ecf\u5178\u7f51\u7edc\u7684\u5206\u6790\u65b9\u6cd5\uff0c\u4f1a\u4e22\u5931\u7ed3\u6784\u4fe1\u606f\u548c\u4e92\u8fde\u7684\u591a\u8def\u590d\u7528\u7f51\u7edc\u4fe1\u606f\u3002\u7531\u6b64\uff0c\u9700\u8981\u6784\u5efa\u4e00\u4e2a\u5f62\u5f0f\u5316\u7684\u6570\u5b66\u6846\u67b6\uff0c\u4ee5\u5904\u7406\u591a\u5c42\u7f51\u7edc\u5f15\u5165\u7684\u590d\u6742\u6027\u3002\u53ef\u80fd\u7684\u5c1d\u8bd5\u5305\u62ec\u4f7f\u7528\u8d85\u77e9\u9635<\/span>\uff08hypermatrics\uff09<\/span>\u53ca\u5f20\u91cf<\/span>\uff08tensor\uff09<\/span>\u3002<\/span><\/section>\n
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\u5176\u6b21\uff0c\u9700\u8981\u6784\u5efa\u591a\u5c42\u62d3\u6251\u5206\u6790\u7684\u65b9\u6cd5\uff0c\u4f8b\u5982\uff0c\u8861\u91cf\u591a\u5c42\u7f51\u7edc\u4e2d\u8282\u70b9\u4e2d\u5fc3\u6027\u6216\u4ecb\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7ec4\u7ec7\u548c\u52a8\u529b\u5b66\uff0c\u4f8b\u5982\uff0c\u7cfb\u7edf\u4e2d\u7684\u4fe1\u606f\u6269\u6563\u6216\u4e34\u754c\u73b0\u8c61\u3001\u5185\u90e8\u6545\u969c\u7684\u540c\u6b65\uff0c\u4ee5\u53ca\u9762\u5bf9\u5916\u90e8\u6270\u52a8\u7684\u9c81\u68d2\u6027\u3002\u5df2\u6709\u4e25\u683c\u8bc1\u660e\u6307\u51fa\uff0c\u4e0d\u80fd\u901a\u8fc7\u5408\u5e76\u5728\u6bcf\u4e00\u5c42\u5355\u72ec\u8ba1\u7b97\u7684\u4e2d\u5fc3\u6027\u6216\u4f7f\u7528\u5728\u5355\u5c42\u7f51\u7edc\u4e2d\u8ba1\u7b97\u7684\u4e2d\u5fc3\u6027\u6765\u5ea6\u91cf\u591a\u5c42\u7f51\u7edc\u7684\u4e2d\u5fc3\u6027\u3002<\/span><\/section>\n
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Battiston, F., Nicosia, V. & Latora, V. Structural measures for multiplex networks. Phys. Rev. E 89, 032804 (2014).<\/section>\n<\/section>\n<\/blockquote>\n
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\u5173\u4e8e\u5728\u4ec0\u4e48\u6761\u4ef6\u4e0b\u9002\u5408\u4f7f\u7528\u591a\u5c42\u7f51\u7edc\u6a21\u578b\uff0c\u5373\u4eba\u4eec\u5e94\u8be5\u5728\u4ec0\u4e48\u65f6\u5019\u5c06\u4e00\u4e2a\u7cfb\u7edf\u5efa\u6a21\u4e3a<\/span>\u591a\u5c42\u7f51\u7edc\uff0c\u800c\u4e0d\u662f\u4e00\u7ec4\u4e92\u4e0d\u76f8\u5e72\u7684\u7f51\u7edc\uff0c\u6216\u8005\u5c06\u6240\u6709\u8282\u70b9\u770b\u6210\u540c\u4e00\u4e2a\u7f51\u7edc\u3002\u5408\u7406\u7684\u5224\u636e\u662f\u5f53\u5c42\u95f4\u8026\u5408\u4e0d\u5f3a\u65f6\uff0c\u6b64\u65f6\u6574\u4e2a\u7cfb\u7edf\u7684\u7279\u6027\u53ef\u4ee5\u4ece\u6bcf\u4e00\u5c42\u9694\u79bb\u7684\u7279\u6027\u7ebf\u6027\u7ec4\u5408\u4e2d\u83b7\u5f97\uff0c\u4e5f\u53ef\u4ee5\u4ece\u5176\u4ed6\u4e00\u4e9b\u7279\u6027\u7684\u805a\u5408\u4e2d\u83b7\u5f97\u3002<\/span><\/section>\n
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Battiston, F., Nicosia, V. & Latora, V. The new challenges of multiplex networks: measures and models. Eur. Phys. J. Special Topics 226, 401\u2013416 (2017).<\/span><\/section>\n<\/section>\n<\/blockquote>\n

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4. \u591a\u5c42\u7f51\u7edc\u7684\u7814\u7a76\u65b9\u5411<\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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4.1 \u6e17\u6d41\u4e0e\u540c\u6b65<\/span><\/strong><\/span><\/section>\n<\/h2>\n
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\u540c\u6b65\u3001\u6e17\u6d41\u662f\u7f51\u7edc\u52a8\u529b\u5b66<\/span>\uff08dynimics\uff09<\/span>\u7684\u7814\u7a76\u70ed\u70b9\u3002\u591a\u5c42\u7f51\u7edc\u95f4\u5b58\u5728\u76f8\u4e92\u5173\u8054\u7684\u540c\u6b65\u73b0\u8c61\uff0c\u5982\u56fe2\u6240\u793a\uff0c\u9ed8\u8ba4\u795e\u7ecf\u7f51\u7edc<\/span>\uff08\u56fe2a-c\uff09<\/span>\u3001\u8179\u4fa7\u90e8\u795e\u7ecf\u5143<\/span>\uff08\u56fe2d-f\uff09<\/span>\u4ee5\u53ca\u89c6\u89c9\u795e\u7ecf\u5143<\/span>\uff08\u56fe2g-i\uff09<\/span>\u7ec4\u6210\u7684\u7f51\u7edc\uff0c\u90fd\u5b58\u5728\u76f8\u4f3c\u7684\u53cc\u7a33\u5b9a\u70b9<\/span>\uff08bistable\uff09<\/span>\u540c\u6b65\u73b0\u8c61\uff0c\u8fd9\u4e9b\u5904\u4e8e\u4e0d\u540c\u4f4d\u7f6e\u7684\u795e\u7ecf\u5143\u7f51\u7edc\u53ef\u4ee5\u770b\u6210\u662f\u591a\u5c42\u7f51\u7edc\u3002\u4e0a\u8ff0\u8fde\u7eed\u7684\u591a\u5c42\u7f51\u7edc\u4e2d\uff0c\u5176\u4e2d\u4e00\u5c42\u7684\u540c\u6b65\u73b0\u8c61\u4fc3\u6210\u4e86\u76f8\u90bb\u7f51\u7edc\u7684\u795e\u7ecf\u5143\u7206\u53d1\u5f0f\u540c\u6b65\u3002<\/span><\/section>\n
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\u56fe2. \u4e0d\u540c\u90e8\u4f4d\u795e\u7ecf\u5143\u7f51\u7edc\u7684\u540c\u6b65\u884c\u4e3a<\/span><\/section>\n
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\u5f53\u591a\u5c42\u7f51\u7edc\u95f4\u5b58\u5728\u8026\u5408\u65f6\uff0c\u7f51\u7edc\u52a8\u529b\u5b66\u540c\u6837\u5448\u73b0\u53cc\u7a33\u6001\u3002\u5982\u56fe 3j \u5c55\u793a\u7684 Kuramoto \u52a8\u529b\u5b66\uff0c\u5176\u4e2d\u8282\u70b9\u4e3a\u632f\u5b50\uff0c\u591a\u5c42\u7f51\u7edc\u7684\u52a8\u529b\u5b66\u53d6\u51b3\u4e8e\u4e0d\u540c\u5c42\u8282\u70b9\u7684\u8026\u5408\u7a0b\u5ea6\u53ca\u504f\u5dee\u3002\u56fe 3k \u5c55\u793a\u4e86\u7f51\u7edc\u6e17\u6d41\u6a21\u578b\u5728\u7f51\u7edc\u4fe1\u606f\u3001\u75be\u75c5\u4f20\u64ad\u73b0\u8c61\u4e0a\u7684\u5e94\u7528\u3002\u901a\u8fc7\u591a\u5c42\u7f51\u7edc\u53ef\u4ee5\u7814\u7a76\u4e24\u79cd\u75c5\u539f\u540c\u65f6\u4f20\u64ad\uff0c\u4e00\u79cd\u75c5\u539f\u7684\u4f20\u64ad\u52a8\u529b\u5b66\u5f71\u54cd\u53e6\u4e00\u79cd\u75c5\u539f\u7684\u771f\u5b9e\u60c5\u51b5\uff1b\u6216\u7814\u7a76\u793e\u4ea4\u5a92\u4f53\u4e0a\u4fe1\u606f\u4f20\u64ad<\/span>\uff08\u56fek\u4e2d\u7684\u989c\u8272\uff09<\/span>\u53d6\u51b3\u4e8e\u4e24\u4e2a\u56e0\u7d20\uff1a\u4e2a\u4f53\u662f\u5426\u613f\u610f\u63a5\u53d7\u4fe1\u606f\uff0c\u662f\u5426\u613f\u610f\u4f20\u64ad\u4fe1\u606f<\/span>\uff08\u5206\u522b\u7528\u5404\u81ea\u7684\u4e00\u5c42\u7f51\u7edc\u5efa\u6a21\uff09<\/span>\uff0c\u4e14\u4e0a\u8ff0\u884c\u4e3a\u5b58\u5728\u76f8\u5173\u6027\u3002<\/span><\/section>\n
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\u56fe3. \u76f8\u4e92\u5173\u8054\u7f51\u7edc\u4e2d\u7684\u52a8\u529b\u5b66<\/span><\/section>\n

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Nicosia, V., Bianconi, G., Latora, V. & Barthelemy, M. Nonlinear growth and condensation in multiplex networks. Phys. Rev. E 90, 042807 (2014).<\/span><\/p>\n


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Gray, C. et al. Ecological plasticity governs ecosystem services in multilayer networks. Commun. Biol. 4, 75 (2021).<\/span><\/section>\n

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Santoro, A., Latora, V., Nicosia, G. & Nicosia, V. Pareto optimality in multilayer network growth. Phys. Rev. Lett. 121, 128302 (2018).<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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4.2 \u5408\u4f5c\u4e0e\u4fe1\u606f\u4f20\u64ad<\/span><\/strong><\/span><\/section>\n<\/h2>\n
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\u66f4\u503c\u5f97\u5173\u6ce8\u7684\u591a\u5c42\u7f51\u7edc\u4e0a\u7684\u535a\u5f08\u4e0e\u5408\u4f5c\u3002\u5f53\u5408\u4f5c\u6536\u76ca\u589e\u52a0\u65f6\uff0c\u4e0d\u540c\u7f51\u7edc\u4e2d\u5408\u4f5c\u8005\u7684\u6bd4\u4f8b\u589e\u52a0\uff0c\u5b58\u5728\u76f8\u53d8\u70b9\uff0c\u5373\u662f\u5426\u5b58\u5728\u5408\u4f5c\u884c\u4e3a\uff0c\u53d6\u51b3\u4e8e\u4e0d\u540c\u5c42\u95f4\u7684\u8026\u5408\u7cfb\u6570<\/span>\uff08\u56fe3l\uff09<\/span>\u3002<\/span><\/section>\n
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\u5c06\u591a\u5c42\u7f51\u7edc\u4e0e\u65f6\u5e8f\u4fe1\u606f\u7ed3\u5408\uff0c\u53ef\u5206\u6790\u76f8\u4e92\u5173\u8054\u7684\u7cfb\u7edf\u4e0a\u7684\u8282\u70b9\u5982\u4f55\u76f8\u4e92\u5f71\u54cd\uff0c\u5bfc\u81f4\u7f51\u7edc\u5931\u6548\u3002\u56fe4a-c\u4ee3\u8868\u4e86\u4e0d\u540c\u65f6\u523b\u610f\u5927\u5229\u7684\u8f93\u7535\u7f51\u53ca\u4e92\u8054\u7f51\u4e2d\u5931\u6548\u8282\u70b9\u7684\u6269\u6563\uff0cd-f\u63cf\u8ff0\u7531\u4e8e\u5355\u8282\u70b9\u5931\u6548\uff0c\u4f20\u64ad\u540e\u5bfc\u81f4\u66f4\u591a\u8282\u70b9\u9010\u6e10\u5931\u6548\u7684\u8fc7\u7a0b\u3002\u4e0e\u5355\u5c42\u795e\u7ecf\u7f51\u7edc\u4e2d\u5f53\u5931\u6548\u7684\u8282\u70b9\u6570\u5927\u4e8e\u9608\u503c\u65f6\u6574\u4e2a\u7f51\u7edc\u4f1a\u5931\u6548\u4e0d\u540c\uff0c\u591a\u5c42\u7f51\u7edc\u4e2d\u7531\u4e8e\u8282\u70b9\u95f4\u7684\u8de8\u5c42\u8fde\u63a5\uff0c\u4f1a\u51fa\u73b0\u4e8c\u9636\u76f8\u53d8\u6216\u5448\u73b0\u8fde\u7eed\u53d8\u5316\uff0c\u8fd9\u4f7f\u5f97\u7f51\u7edc\u6062\u590d\u3001\u653b\u51fb\u7b56\u7565\u53d8\u5f97\u66f4\u4e3a\u590d\u6742\uff0c\u591a\u91cd\u7f51\u7edc\u4e2d\u5b58\u5728\u8de8\u8fde\u63a5\u7684\u4e09\u91cd\u70b9<\/span>\uff08triple points\uff09<\/span>\u5c06\u6210\u4e3a\u7f51\u7edc\u4fee\u590d\u7b56\u7565\u4e2d\u7684\u5173\u952e\u3002<\/span><\/section>\n
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Gray, C. et al. Ecological plasticity governs ecosystem services in multilayer networks. Commun. Biol. 4, 75 (2021).<\/span><\/section>\n<\/section>\n<\/blockquote>\n
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4.3 \u4ecb\u89c2\u7ec4\u7ec7\u3001\u7ed3\u6784\u4e0e\u529f\u80fd<\/span><\/strong><\/span><\/section>\n<\/h2>\n
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\u56fe6. \u4f7f\u7528\u591a\u5c42\u7f51\u7edc\u7684\u8868\u5f81\uff0c\u4e00\u4e2a\u590d\u6742\u7cfb\u7edf\u53ef\u4ee5\u6709\u5197\u4f59\u7684\u5c42\uff0c\u65b0\u589e\u7684\u5c42\u4e0d\u6dfb\u52a0\u62d3\u6251\u6216\u529f\u80fd\u4fe1\u606f\uff0c\u901a\u8fc7\u8fde\u901a\u6027\u76f8\u4f3c\u5ea6\u805a\u7c7b\uff0c\u57fa\u4e8e\u51af\u00b7\u8bfa\u4f0a\u66fc\u71b5\u7b49\u65b9\u5f0f\uff0c\u53ef\u5c06\u591a\u5c42\u7f51\u7edc\u7c97\u7c92\u5316<\/span><\/p>\n

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\u4f8b\u5982\u5728\u7814\u7a76\u75be\u75c5\u4f20\u64ad\u65f6\uff0c\u4e0d\u4ec5\u8003\u8651\u4eba\u4e0e\u4eba\u7684\u6d41\u52a8\uff0c\u4e5f\u8003\u8651\u901a\u8baf\u4fe1\u606f\u5bf9\u75be\u75c5\u4f20\u64ad\u7684\u5f71\u54cd\uff0c\u4ece\u800c\u8fdb\u884c\u66f4\u7cbe\u51c6\u7684\u5efa\u6a21\u3002\u5982\u56fe8a\u6240\u793a\uff0c\u5206\u522b\u4e3a\u4eba\u5458\u79fb\u52a8\u7f51\u7edc\u548c\u901a\u4fe1\u7f51\u7edc\uff0c\u5728\u6b64\u4e4b\u4e0a\u5b58\u5728\u7b2c\u4e09\u79cd\u52a8\u529b\u5b66\uff0c\u5373\u75be\u75c5\u4f20\u64ad\u7f51\u7edc\u3002\u56fe8b\u6309\u7167\u805a\u96c6\u65b9\u5f0f\u5c55\u793a\u4e86\u5b66\u6821\u3001\u793e\u533a\u3001\u5bb6\u5ead\u3001\u5de5\u4f5c\u573a\u6240\u7684\u4eba\u5458\u6d41\u52a8\uff0c\u901a\u8fc7\u5206\u5f00\u5904\u7406\uff0c\u53ef\u4ee5\u8003\u5bdf\u4eba\u5458\u805a\u96c6\u7684\u5e74\u9f84\u7279\u5f81<\/span>\uff08\u56fe8c\uff09<\/span>\u3002<\/span><\/section>\n
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\u56fe8. \u4f7f\u7528\u591a\u91cd\u7f51\u7edc\u7814\u7a76\u75be\u75c5\u4f20\u64ad<\/span><\/section>\n
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Calhoun, V. D., Miller, R., Pearlson, G. & Adal\u0131, T. The chronnectome: time-varying connectivity networks as the next frontier in fMRI data discovery. Neuron 84, 262\u2013274 (2014).<\/span><\/p>\n


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Valdano, E., Ferreri, L., Poletto, C. & Colizza, V. Analytical computation of the epidemic threshold on temporal networks. Phys. Rev. X 5, 021005 (2015).<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u7531\u7535\u5b50\u79d1\u6280\u5927\u5b66\u5415\u7433\u5a9b\u8001\u5e08\u3001\u4efb\u6653\u9f99\u8001\u5e08\u53ca\u4e2d\u56fd\u5730\u8d28\u5927\u5b66\uff08\u5317\u4eac\uff09\u7ba1\u9752\u8001\u5e08\u5728\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u53d1\u8d77\u4e86\u3010\u9ad8\u9636\u7f51\u7edc\u8bfb\u4e66\u4f1a<\/a>\u3011\u3002\u8bfb\u4e66\u4f1a\u56f4\u7ed5\u9ad8\u9636\u4ea4\u4e92\u7f51\u7edc\u7684\u57fa\u672c\u6982\u5ff5\u3001\u6a21\u578b\u3001\u65b9\u6cd5\u4e0e\u5e94\u7528\u7b49\u7814\u7a76\u8fdb\u884c\u7814\u8ba8\uff0c\u6309\u7167\u300c\u57fa\u7840\u7406\u8bba\u300d+\u300c\u6df1\u5165\u7406\u8bba\u300d+\u300c\u6848\u4f8b\u7814\u8ba8\u300d\u7684\u6a21\u5f0f\u5c55\u5f00\u3002\u8bfb\u4e66\u4f1a\u7b2c\u4e00\u5b63\u5df2\u7ecf\u5706\u6ee1\u7ed3\u675f\uff0c\u7b2c\u4e8c\u5b63\u6b63\u5728\u7b79\u5907\u4e2d\u3002\u73b0\u5728\u62a5\u540d\u52a0\u5165\u53ef\u4ee5\u89e3\u9501\u7b2c\u4e00\u5b63\u5168\u90e8\u5f55\u64ad\u89c6\u9891\u5e76\u52a0\u5165\u793e\u7fa4\u4ea4\u6d41\u3002<\/span><\/section>\n


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1.  <\/strong>\u5927\u8111\u7f51\u7edc\u7ec4\u7ec7\u7684\u591a\u5c3a\u5ea6\u5efa\u6a21\uff1a\u591a\u5c42\u7f51\u7edc\u89c6\u89d2<\/a><\/strong><\/span><\/strong><\/section>\n
2.<\/strong>  Barab\u00e1si\u56e2\u961f\u6700\u65b0\u7814\u7a76\uff1a\u591a\u5c42\u7f51\u7edc\u4e2d\u7684\u6062\u590d\u8026\u5408\u673a\u5236<\/a>  <\/strong><\/span><\/section>\n
3.  <\/strong><\/strong><\/a>\u739b\u4e3d\u5973\u738b\u5927\u5b66 Ginestra Bianconi\uff1a\u9ad8\u9636\u7f51\u7edc\u7684\u62d3\u6251\u7ed3\u6784\u4e0e\u52a8\u529b\u5b66<\/a><\/strong><\/strong><\/span><\/strong><\/section>\n
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5. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/a><\/span><\/strong><\/section>\n
7. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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