{"id":35637,"date":"2022-07-03T22:57:53","date_gmt":"2022-07-03T14:57:53","guid":{"rendered":"https:\/\/swarma.org\/?p=35637"},"modified":"2022-07-03T22:57:53","modified_gmt":"2022-07-03T14:57:53","slug":"%e9%95%bf%e6%96%87%e7%bb%bc%e8%bf%b0%ef%bc%9a%e5%a4%a7%e8%84%91%e4%b8%ad%e7%9a%84%e7%86%b5%e3%80%81%e8%87%aa%e7%94%b1%e8%83%bd%e3%80%81%e5%af%b9%e7%a7%b0%e6%80%a7%e5%92%8c%e5%8a%a8%e5%8a%9b%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=35637","title":{"rendered":"\u957f\u6587\u7efc\u8ff0\uff1a\u5927\u8111\u4e2d\u7684\u71b5\u3001\u81ea\u7531\u80fd\u3001\u5bf9\u79f0\u6027\u548c\u52a8\u529b\u5b66"},"content":{"rendered":"
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Viktor Jirsa, Hiba Sheheitli<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/span><\/p>\n

JawDrin<\/span><\/strong> <\/span>| <\/strong><\/span>\u8bd1\u8005<\/strong><\/strong><\/span><\/p>\n

\u5f6d\u83d8\u5cfb<\/span><\/strong><\/strong> <\/span>| <\/strong><\/span>\u5ba1\u6821<\/strong><\/strong><\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea <\/span>| <\/strong><\/span>\u7f16\u8f91<\/strong><\/span><\/p>\n<\/section>\n


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Entropy, Free Energy, Symmetry and Dynamics in the Brain<\/span><\/p>\n

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https:\/\/iopscience.iop.org\/article\/10.1088\/2632-072X\/ac4bec\/meta<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6458\u8981\uff1a<\/span><\/strong>\u795e\u7ecf\u79d1\u5b66\u662f\u6839\u690d\u4e8e\u5404\u79cd\u9886\u57df\u7684\u6982\u5ff5\u53ca\u7406\u8bba\u7684\u5bb6\u56ed\uff0c\u5305\u62ec\u4fe1\u606f\u8bba\u3001\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u548c\u8ba4\u77e5\u5fc3\u7406\u5b66\u3002\u4f46\u5e76\u975e\u6240\u6709\u7684\u9886\u57df\u90fd\u53ef\u4ee5\u8fde\u8d2f\u5730\u8054\u7cfb\u8d77\u6765\uff0c\u6709\u4e9b\u6982\u5ff5\u662f\u4e0d\u53ef\u901a\u7ea6\u7684\uff0c\u800c\u4e14\u7279\u5b9a\u9886\u57df\u7684\u672f\u8bed\u7ed9\u6574\u5408\u5e26\u6765\u969c\u788d\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u6982\u5ff5\u6574\u5408\u4ecd\u7136\u662f\u63d0\u4f9b\u76f4\u89c9\u548c\u5de9\u56fa\u7684\u7406\u89e3\u5f62\u5f0f\uff0c\u6ca1\u6709\u6982\u5ff5\u6574\u5408\uff0c\u8fdb\u5c55\u5c06\u662f\u65e0\u5934\u82cd\u8747\u3002\u672c\u6587\u5173\u6ce8\u5728\u4fe1\u606f\u8bba\u6846\u67b6\u5185\u6574\u5408\u786e\u5b9a\u6027\u8fc7\u7a0b\u548c\u968f\u673a\u6027\u8fc7\u7a0b\uff0c\u4ece\u800c\u5c06\u4fe1\u606f\u71b5\u548c\u81ea\u7531\u80fd\u4e0e\u8111\u7f51\u7edc\u4e2d\u7684\u6d8c\u73b0\u52a8\u529b\u5b66\u673a\u5236\u548c\u81ea\u7ec4\u7ec7\u673a\u5236\u8054\u7cfb\u8d77\u6765\u3002\u6211\u4eec\u786e\u5b9a\u4e86\u795e\u7ecf\u5143\u7fa4<\/span>\uff08neuronal populations\uff09<\/span>\u7684\u57fa\u672c\u5c5e\u6027\uff0c\u8be5\u5c5e\u6027\u5bfc\u81f4\u7b49\u53d8\u77e9\u9635\u51fa\u73b0\u5728\u7f51\u7edc\u4e2d\uff0c\u800c\u5728\u8be5\u7f51\u7edc\u4e2d\uff0c\u590d\u6742\u884c\u4e3a\u53ef\u4ee5\u901a\u8fc7\u6d41\u5f62\u4e0a\u7684\u7ed3\u6784\u5316\u6d41\u6765\u8868\u793a\uff0c\u4ece\u800c\u5efa\u7acb\u4e0e\u8111\u529f\u80fd\u7406\u8bba\u76f8\u5173\u7684\u5185\u90e8\u6a21\u578b\u3002\u6211\u4eec\u63d0\u51fa\u4e00\u79cd\u4ece\u8111\u7f51\u7edc\u8fde\u63a5\u7684\u5bf9\u79f0\u6027\u7834\u7f3a\u4e2d\u751f\u4ea7\u5185\u90e8\u6a21\u578b\u7684\u795e\u7ecf\u673a\u5236\u3002\u6d8c\u73b0\u7684\u89c2\u70b9\u8bf4\u660e\u4e86\u81ea\u7531\u80fd\u5982\u4f55\u4e0e\u5185\u90e8\u6a21\u578b\u8054\u7cfb\u8d77\u6765\uff0c\u4ee5\u53ca\u5b83\u4eec\u5982\u4f55\u7531\u795e\u7ecf\u5e95\u5c42\u4e2d\u4ea7\u751f\u3002<\/span><\/section>\n

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\u9884\u6d4b\u7f16\u7801<\/span>\uff08Predictive coding\uff09<\/span>\u662f\u5f53\u4ee3\u6700\u5177\u5f71\u54cd\u529b\u7684\u8111\u529f\u80fd\u7406\u8bba\u4e4b\u4e00[1-3]\u3002\u8be5\u7406\u8bba\u57fa\u4e8e\u5927\u8111\u4f5c\u4e3a\u8d1d\u53f6\u65af\u63a8\u7406\u7cfb\u7edf\u8fd0\u884c\u8fd9\u4e00\u76f4\u89c9\uff0c\u5982\u6b64\u5b9e\u73b0\u5185\u90e8\u751f\u6210\u6a21\u578b\u5bf9\u5916\u90e8\u4e16\u754c\u7684\u9884\u6d4b\u3002\u8fd9\u4e9b\u9884\u6d4b\u4e0d\u65ad\u5730\u4e0e\u611f\u5b98\u8f93\u5165\u8fdb\u884c\u5bf9\u6bd4\uff0c\u5f62\u6210\u9884\u6d4b\u8bef\u5dee\u5e76\u66f4\u65b0\u5185\u90e8\u6a21\u578b<\/span>\uff08\u89c1\u56fe1\uff09<\/span>\u3002\u4ece\u7406\u8bba\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u7528\u9884\u6d4b\u7f16\u7801\u7684\u5f62\u5f0f\u8868\u793a\u8111\u529f\u80fd\u662f\u5982\u6b64\u8ff7\u4eba\uff0c\u56e0\u4e3a\u8fd9\u89e3\u51b3\u4e86\u4e0d\u540c\u9886\u57df\u8fc7\u591a\u7684\u6df1\u5965\u6982\u5ff5\u3002\u8fd9\u6837\u4fbf\u6709\u673a\u4f1a\u5c06\u62bd\u8c61\u6982\u5ff5\u8054\u7cfb\u8fdb\u4e00\u4e2a\u6574\u5408\u6846\u67b6\u5185\uff0c\u8fd9\u4e9b\u62bd\u8c61\u6982\u5ff5\u5982\u52a8\u529b\u5b66\u3001\u786e\u5b9a\u6027\u4f5c\u7528\u548c\u968f\u673a\u6027\u4f5c\u7528\u3001\u6d8c\u73b0\u3001\u81ea\u7ec4\u7ec7[4-6]\u3001\u4fe1\u606f\u3001\u71b5\u3001\u81ea\u7531\u80fd[7,8]\u3001\u7a33\u6001\u7b49\u7b49\u3002\u8be5\u8de8\u9886\u57df\u7684\u6574\u5408\u7b26\u5408\u5bf9\u8fd9\u4e9b\u590d\u6742\u62bd\u8c61\u6982\u5ff5\u7684\u76f4\u89c2\u7406\u89e3\uff0c\u5c3d\u7ba1\u901a\u5e38\u4e3a\u4fdd\u7559\u6613\u5904\u7406\u6027\uff0c\u5bf9\u4e8e\u7ed9\u5b9a\u6982\u5ff5\u7684\u6240\u6709\u590d\u6742\u6027\u5c42\u9762\u6ca1\u6709\u5168\u90e8\u88ab\u7b49\u4ef7\u5730\u523b\u753b\u3002\u4f8b\u5982\uff0c\u5728\u9884\u6d4b\u7f16\u7801\u7406\u8bba\u4e2d\u4f7f\u7528\u7b80\u5355\u7684\u5185\u90e8\u6a21\u578b<\/span>\uff08\u5982\u5728\u505a\u51b3\u7b56\u65f6\uff0c\u52a8\u529b\u5b66\u88ab\u7b80\u5316\u4e3a\u8f6c\u6362\uff09<\/span>\uff0c\u4f46\u662f\u7b80\u5355\u7684\u6a21\u578b\u5f88\u96be\u63a8\u5e7f\u5230\u66f4\u590d\u6742\u7684\u884c\u4e3a\u3002\u5f53\u7126\u70b9\u5728\u8fc7\u7a0b\u7684\u63a8\u7406\u90e8\u5206\u65f6\uff0c\u8fd9\u79cd\u505a\u6cd5\u7406\u6240\u5f53\u7136\uff0c\u800c\u6211\u4eec\u4e0d\u5e0c\u671b\u8fd9\u6837\u505a\u3002\u5b9e\u9645\u4e0a\u6211\u4eec\u5f3a\u8c03\u5185\u90e8\u6a21\u578b\u5728\u5927\u8111\u6fc0\u6d3b\u65b9\u9762\u7684\u795e\u7ecf\u57fa\u7840\u4ee5\u53ca\u8981\u4e0e\u590d\u6742\u884c\u4e3a\u6d8c\u73b0\u7684\u7406\u8bba\u76f8\u8054\u7cfb\u3002\u4e0d\u8fc7\uff0c\u8003\u8651\u5230\u4fe1\u606f\u8bba\u6982\u5ff5<\/span>\uff08\u5c24\u5176\u662f\u71b5\u548c\u81ea\u7531\u80fd\uff09<\/span>\u7684\u91cd\u8981\u6027\uff0c\u5728\u9884\u6d4b\u7f16\u7801\u65b9\u9762\uff0c\u8fd9\u6837\u7684\u5c1d\u8bd5\u8981\u6c42\u5b83\u4eec\u4e0e\u5f53\u4ee3\u8111\u7f51\u7edc\u6a21\u578b\u4e2d\u5b58\u5728\u7684\u6982\u7387\u5206\u5e03\u51fd\u6570\u548c\u76f8\u5173\u7684\u786e\u5b9a\u6027\u4f5c\u7528\u548c\u968f\u673a\u6027\u4f5c\u7528\u8fdb\u884c\u6574\u5408<\/span>\uff08\u76f8\u5173\u89c2\u70b9\u540c\u89c1[9-11]\uff09<\/span>\u3002<\/span><\/section>\n

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\u56fe1\uff1a\u8d1d\u53f6\u65af\u5927\u8111\u5047\u8bf4\uff08Bayesian brain hypothesis\uff09\u7684\u63a8\u7406\u8fc7\u7a0b\u56fe\u793a\u3002\u56fe\u5de6\u4fa7\u7684\u751f\u6210\u6a21\u578b\u8868\u73b0\u4e3a\u5185\u90e8\u795e\u7ecf\u52a8\u529b\u5b66\uff0c\u901a\u8fc7\u611f\u77e5\u548c\u884c\u52a8\uff08\u56fe\u53f3\u4fa7\uff09\u4e0e\u5916\u90e8\u4e16\u754c\u8fdb\u884c\u4fe1\u606f\u4ea4\u6362\u6765\u5b9e\u73b0\u6a21\u578b\u66f4\u65b0\u3002<\/span><\/p>\n


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Karl Friston\u9996\u6b21\u63d0\u51fa\u628a\u81ea\u7531\u80fd\u4f5c\u4e3a\u5927\u8111\u529f\u80fd\u7684\u4e00\u4e2a\u539f\u5219[12-14]\uff0c\u4ece\u6570\u5b66\u4e0a\u9610\u8ff0\u4e86\u81ea\u9002\u5e94\u3001\u81ea\u7ec4\u7ec7\u7cfb\u7edf\u5982\u4f55\u62b5\u6297\u81ea\u7136\u7684<\/span>\uff08\u70ed\u529b\u5b66\u7684\uff09<\/span>\u65e0\u5e8f\u503e\u5411\u3002\u968f\u7740\u65f6\u95f4\u63a8\u79fb\uff0c\u81ea\u7531\u80fd\u539f\u7406\u5df2\u7ecf\u4ece\u8d6b\u59c6\u970d\u5179\u673a<\/span>\uff08Helmholtz machine\uff09<\/span>\u4e2d\u4f7f\u7528\u7684\u81ea\u7531\u80fd\u6982\u5ff5\u91cc\u53d1\u5c55\u51fa\u6765\uff0c\u5728\u9884\u6d4b\u7f16\u7801\u80cc\u666f\u4e0b\u7528\u6765\u89e3\u91ca\u5927\u8111\u76ae\u5c42\u53cd\u5e94\uff0c\u5e76\u9010\u6e10\u53d1\u5c55\u4e3a\u667a\u80fd\u4f53\u7684\u4e00\u822c\u539f\u5219\uff0c\u8fd9\u4e5f\u88ab\u79f0\u4e3a\u4e3b\u52a8\u63a8\u7406[15]\u3002\u8d1d\u53f6\u65af\u63a8\u7406\u8fc7\u7a0b\u548c\u6700\u5927\u4fe1\u606f\u51c6\u5219\uff08maximum information principle\uff09\u4e24\u8005\u5b9e\u9645\u4e0a\u90fd\u53ef\u91cd\u65b0\u9610\u8ff0\u4e3a\u81ea\u7531\u80fd\u6700\u5c0f\u5316\u95ee\u9898<\/strong>\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u5173\u4e8e\u81ea\u7531\u80fd\u7684\u6982\u5ff5\u5728\u4e24\u4e2a\u76f8\u5173\u7684\u6846\u67b6\u4e2d\u90fd\u6709\u4f7f\u7528\uff0c\u4f46\u5b83\u4eec\u5e76\u4e0d\u5b8c\u5168\u7b49\u4ef7\u3002\u6a21\u68f1\u4e24\u53ef\u6216\u56e0\u4e3a\u8fd9\u6837\u7684\u4e8b\u5b9e\uff0c\u5373\u5b83\u4eec\u7684\u4e00\u822c\u5f62\u5f0f\u7c7b\u4f3c\u4e8e\u70ed\u529b\u5b66\u4ea5\u59c6\u970d\u5179\u81ea\u7531\u80fd<\/span>\uff08Helmholtz free energy\uff09<\/span>\uff0c\u4f46\u662f\u5374\u6765\u81ea\u4e8e\u4e24\u79cd\u4e0d\u540c\u7684\u63a8\u7406\u8def\u7ebf<\/span>\uff08\u8be6\u89c1[15]\uff09<\/span>\u3002\u7b2c\u4e00\u4e2a\u662f\u6240\u8c13\u7684\u201c\u6765\u81ea\u7ea6\u675f\u7684\u81ea\u7531\u80fd\u201d\uff0c\u5bf9\u5e94\u4e8e\u6700\u5927\u4fe1\u606f\u51c6\u5219\u4e0b\u6700\u5c0f\u5316\u7684\u81ea\u7531\u80fd\uff0c\u8868\u793a\u786e\u5b9a\u6027\u7ea6\u675f\u548c\u968f\u673a\u4f5c\u7528\u4e4b\u95f4\u7684\u6743\u8861[7]\u3002\u6211\u4eec\u4e3b\u8981\u8003\u8651\u7684\u4fbf\u662f\u8fd9\u79cd\u7c7b\u578b\u7684\u81ea\u7531\u80fd\u53ca\u5176\u7ea6\u675f\u3002\u53e6\u4e00\u4e2a\u662f\u53d8\u5206\u81ea\u7531\u80fd<\/span>\uff08variational free energy\uff09<\/span>\u5e76\u4e0e\u8d1d\u53f6\u65af\u5927\u8111\u5047\u8bf4\u6709\u5173\u3002\u8fd9\u79cd\u81ea\u7531\u80fd\u6982\u5ff5\u6e90\u4e8e\u5bf9\u8d1d\u53f6\u65af\u89c4\u5219\u7684\u91cd\u65b0\u8868\u8ff0\uff0c\u5373\u8868\u8ff0\u4e3a\u5bfb\u627e\u6700\u5c0f\u5316\u76f8\u5bf9\u71b5<\/span>\uff08KL-\u6563\u5ea6\uff09<\/span>\u7684\u6982\u7387\u5206\u5e03\u8fd9\u4e00\u4f18\u5316\u95ee\u9898\uff0c\u5176\u4e2d\u76f8\u5bf9\u71b5\u8868\u793a\u504f\u79bb\u7cbe\u786e\u8d1d\u53f6\u65af\u540e\u9a8c\u7684\u8bef\u5dee\u3002<\/span><\/section>\n

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\u786e\u5b9a\u7ea6\u675f\u5728\u6d41\u5f62\u4e0a\u7684\u7ed3\u6784\u5316\u6d41<\/strong><\/span>\uff08structured flows on manifolds, SFMs\uff09<\/span>[16,17]\u6846\u67b6\u4e2d\u4ee5\u52a8\u529b\u5b66\u7684\u5f62\u5f0f\u8868\u793a\uff0c\u5176\u4e2d\u7ed3\u6784\u5316\u6d41\u5c5e\u4e8e\u7f51\u7edc\u4e2d\u4ea7\u751f\u7684\u4f4e\u7ef4\u52a8\u529b\u7cfb\u7edf\uff0c\u56e0\u6b64\u662f\u5927\u8111\u7406\u8bba\u4e2d\u8868\u793a\u5185\u90e8\u6a21\u578b\u7684\u4e3b\u8981\u5019\u9009\u8005\u3002\u901a\u8fc7\u6982\u7387\u5206\u5e03\u7684\u4ecb\u5bfc\uff0c\u7ecf\u9a8c\u53ef\u5f97\u7684\u51fd\u6570<\/span>\uff08\u5982\u653e\u7535\u7387\u3001\u80fd\u91cf\u3001\u65b9\u5dee\u7b49\u7b49\uff09<\/span>\u4e0a\u7684\u76f8\u5173\u6027\u90fd\u542b\u6709\u81ea\u7531\u80fd\u548cSFMs\u4e24\u8005\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u5176\u4e2d\uff0c\u6982\u7387\u5206\u5e03\u5728\u7cfb\u7edf\u4e2d\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u4f5c\u7528\u7684\u76f8\u4e92\u4f5c\u7528\u4e0b\u5f62\u6210\u3002Ilya Prigogine \u5728\u9610\u8ff0\u71b5\u7684\u542b\u4e49\u65f6\uff0c\u8be6\u7ec6\u8bf4\u660e\u4e86\u8fd9\u4e9b\u4f5c\u7528\u4e4b\u95f4\u7684\u7d27\u5bc6\u8054\u7cfb\u3002\u5728\u8fd9\u91cc\uff0c\u65f6\u95f4<\/span>\uff08\u7684\u6982\u5ff5\uff09<\/span>\u8d85\u8d8a\u4e86\u91cd\u590d\u548c\u9000\u5316\u7684\u6982\u5ff5\uff0c\u8fbe\u5230\u5efa\u8bbe\u6027\u7684\u4e0d\u53ef\u9006\u6027\u6982\u5ff5\uff0c\u5982\u751f\u547d\u7cfb\u7edf\u6240\u8868\u73b0\u7684\u90a3\u6837\uff0c\u901a\u8fc7\u4e0e\u5176\u6240\u5904\u7684\u73af\u5883\u8fdb\u884c\u71b5\u7684\u4ea4\u6362\u6765\u6c38\u5b58\u81ea\u5df1\u3002\u751f\u7269\u5b66\u88ab\u8ba4\u4e3a\u9700\u8981\u5c06\u4e0d\u53ef\u9006\u7684\u65f6\u95f4\u523b\u5728\u7269\u8d28\u4e4b\u4e0a\u3002\u5728\u795e\u7ecf\u79d1\u5b66\u7684\u80cc\u666f\u4e0b\uff0c\u8fd9\u8ba9\u6211\u4eec\u60f3\u8d77Ingvar\u7684\u5047\u5b9a\uff0c\u5373\u5927\u8111\u6709\u80fd\u529b\u901a\u8fc7\u5176\u65f6\u95f4\u6781\u5316\u7ed3\u6784\u6a21\u62df\u201c\u5c06\u6765\u7684\u8bb0\u5fc6\u201d[20]\uff0c\u4ee5\u53ca\u5927\u8111\u80fd\u7ef4\u6301\u548c\u5bfc\u822a\u5206\u5e03\u5728\u4e0d\u540c\u8111\u533a\u7684\u8fc7\u53bb\u3001\u73b0\u5728\u548c\u5c06\u6765\u7684\u7ecf\u9a8c\u3002<\/span><\/section>\n

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\u5c3d\u7ba1\u71b5\u7684\u6570\u5b66\u516c\u5f0f\u6700\u5148\u51fa\u73b0\u5728\u7ecf\u5178\u70ed\u529b\u5b66<\/span>\uff08\u6d89\u53ca\u8bf8\u5982\u70ed\u3001\u6e29\u5ea6\u548c\u80fd\u91cf\u4ea4\u6362\u7b49\u5b8f\u89c2\u91cf\uff09<\/span>\u7684\u80cc\u666f\u4e0b\uff0c\u4e4b\u540e\u7684\u7edf\u8ba1\u529b\u5b66\u5c06\u71b5\u8868\u793a\u4e3a\u7cfb\u7edf\u5904\u4e8e\u4e0d\u540c\u53ef\u80fd\u5fae\u89c2\u72b6\u6001\u7684\u6982\u7387\u5bf9\u6570\u51fd\u6570\u3002\u540e\u8005\u7684\u51fd\u6570\u5f62\u5f0f\u4e0e\u9999\u519c\u4fe1\u606f\u71b5\u76f8\u540c\uff0c\u5176\u4e2d\uff0c\u9999\u519c\u4fe1\u606f\u71b5\u8868\u8fbe\u5f0f\u4e2d\u7684\u6982\u7387\u662f\u53d8\u91cf\u7684\u4e0d\u540c\u53ef\u80fd\u53d6\u503c\u7684\u6982\u7387<\/span>\uff08\u89c12.2\u8282\uff09<\/span>\u3002\u5982 Edwin T Jaynes \u57281957\u5e74\u6240\u8bf4\u90a3\u6837\uff0c\u5728\u66f4\u6df1\u5c42\u6b21\u4e0a\uff0c\u4f5c\u4e3a\u7528\u6982\u7387\u5206\u5e03\u8868\u793a\u7684\u4e0d\u786e\u5b9a\u6027\u5ea6\u91cf\uff0c\u8fd9\u4e24\u79cd\u71b5\u7684\u6982\u5ff5\u7d27\u5bc6\u8054\u7cfb\uff1b\u5728\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0c\u90fd\u88ab\u89c6\u4e3a\u53d7\u89c2\u6d4b\u91cf\u7ea6\u675f\u7684\u6982\u7387\u5206\u5e03\u7684\u9884\u6d4b\u95ee\u9898\uff0c\u5176\u4e2d\u5177\u6709\u6700\u5927\u71b5\u7684\u6982\u7387\u5206\u5e03\u662f\u552f\u4e00\u7684\u65e0\u504f\u9009\u62e9[7]\u3002<\/span><\/section>\n

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\u4e0a\u8ff0\u5173\u4e8e\u71b5\u542b\u4e49\u7684\u7b80\u77ed\u8bba\u8ff0\uff0c\u5728 Hermann Haken \u5efa\u7acb\u7684\u534f\u540c\u5b66<\/span>\uff08synergetics\uff09<\/span>\u4e2d\u627e\u5230\u4e00\u4e2a\u7406\u8bba\u6846\u67b6\uff0c\u8be5\u6846\u67b6\u6b63\u5f0f\u96c6\u6210\u4e86\u8fdc\u79bb\u5e73\u8861\u7cfb\u7edf<\/span>\uff08far-from-equilibrium systems\uff09<\/span>\u4e2d\u8017\u6563\u7ed3\u6784<\/span>\uff08dissipative structures\uff09<\/span>\u6d8c\u73b0\u7684\u6570\u5b66\u5f62\u5f0f\u3002\u975e\u7ebf\u6027\u548c\u4e0d\u7a33\u5b9a\u6027\u5bfc\u81f4\u6d8c\u73b0\u548c\u590d\u6742\u6027\u673a\u5236\u7684\u4ea7\u751f\uff0c\u800c\u71b5\u548c\u6da8\u843d\u5bfc\u81f4\u4e0d\u53ef\u9006\u6027\u548c\u4e0d\u53ef\u9884\u6d4b\u6027\u3002\u8fd9\u79cd\u52a8\u529b\u5b66\u7684\u672c\u8d28\u81ea\u7136\u4f1a\u5f15\u51fa\u6982\u7387\u6982\u5ff5\uff0c\u5f25\u8865\u4e86\u6211\u4eec\u65e0\u6cd5\u7cbe\u786e\u523b\u753b\u51fa\u7cfb\u7edf\u7684\u72ec\u7279\u8f68\u8ff9\u3002\u534f\u540c\u5b66\u4e00\u76f4\u662f\u5c06\u8fd9\u4e9b\u539f\u5219\u63a8\u53ca\u5176\u5b83\u9886\u57df\u7684\u9a71\u52a8\u529b\uff0c\u5c24\u5176\u662f\u751f\u547d\u79d1\u5b66\u548c\u795e\u7ecf\u79d1\u5b66\u3002\u7406\u6e05\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u5f71\u54cd\u7684\u4e8c\u5143\u6027\u5e76\u8be6\u8ff0\u5176\u5982\u4f55\u5728\u5927\u8111\u4e2d\u4ea7\u751f\uff0c\u5c06\u4f1a\u4e3a\u6211\u4eec\u7684\u613f\u666f\u521b\u9020\u821e\u53f0\u3002\u56e0\u6b64\uff0c\u672c\u6587\u7684\u76ee\u6807\u4fbf\u662f\u89e3\u5f00\u540e\u9762\u8fd9\u4e9b\u590d\u6742\u7684\u5173\u7cfb\uff0c\u4ece\u800c\u7edf\u4e00\u770b\u4f3c\u65e0\u5173\u7684\u5927\u8111\u52a8\u529b\u5b66\u6a21\u578b\u6846\u67b6\u3002<\/span><\/section>\n

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\u8003\u8651\u5230\u8fd9\u4e9b\u6982\u5ff5\u7684\u4e92\u8865\u6027\uff0c\u4e14\u4e3a\u65b9\u4fbf\u6765\u81ea\u4e0d\u540c\u80cc\u666f\u7684\u5bf9\u5b8f\u89c2\u5927\u8111\u52a8\u529b\u5b66\u5efa\u6a21\u611f\u5174\u8da3\u7684\u8bfb\u8005\uff0c\u6211\u4eec\u5148\u9000\u4e00\u6b65\uff0c\u56de\u987e\u4e00\u4e9b\u6982\u7387\u8bba\u548c\u4fe1\u606f\u8bba\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u3002<\/span><\/section>\n

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Edwin T Jaynes\u5f3a\u8c03\uff0c\u4fe1\u606f\u8bba\u7684\u91cd\u5927\u6982\u5ff5\u8fdb\u6b65\u5728\u4e8e\u6709\u4e00\u4e2a\u660e\u786e\u7684\u91cf\uff0c\u5373\u5229\u7528\u6982\u7387\u5206\u5e03\u6765\u8868\u793a\u4e0d\u786e\u5b9a\u6027\u6570\u91cf\u7684\u4fe1\u606f\u71b5\uff0c\u76f4\u89c2\u53cd\u6620\u4e86\u5bbd\u5206\u5e03\u6bd4\u5c16\u5cf0\u5206\u5e03\u4ee3\u8868\u66f4\u591a\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u540c\u65f6\u4e5f\u6ee1\u8db3\u4e0e\u8be5\u76f4\u89c9\u4e00\u81f4\u7684\u5176\u5b83\u6240\u6709\u6761\u4ef6[7]\u3002\u5728\u65e0\u4efb\u4f55\u4fe1\u606f\u7684\u60c5\u51b5\u4e0b\uff0c\u5bf9\u5e94\u7684\u6982\u7387\u5206\u5e03\u5b8c\u5168\u65e0\u4fe1\u606f\u800c\u4e14\u71b5\u4fe1\u606f\u6d88\u5931\u3002\u5728\u6709\u4e00\u4e9b\u786e\u5b9a\u6027\u7ea6\u675f\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u7269\u7406\u89c2\u6d4b\u91cf\u5747\u503c\u7684\u6d4b\u91cf\u503c\uff0c\u5229\u7528\u7b2c\u4e00\u7c7b\u62c9\u683c\u6717\u65e5\u65b9\u7a0b<\/span>\uff08Lagrange’s theory of first kind\uff09<\/span>\uff0c\u6211\u4eec\u53ef\u4ee5\u6c42\u89e3\u8be5\u7ea6\u675f\u4e0b\u5bf9\u5e94\u7684\u6700\u5927\u5316\u4fe1\u606f\u71b5<\/span>\uff08\u7b49\u6548\u4e8e\u6700\u5c0f\u5316\u81ea\u7531\u80fd[7,12]\uff09<\/span>\u7684\u6982\u7387\u5206\u5e03\u3002\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0c\u5bf9\u71b5\u7684\u8003\u91cf\u4f18\u5148\u4e8e\u5bf9\u786e\u5b9a\u6027\u5f71\u54cd\u7684\u8ba8\u8bba\uff0c\u800c\u4e14\u65ad\u5b9a\u5e94\u7b26\u5408\u6700\u5927\u71b5\u5206\u5e03\uff0c\u8be5\u65ad\u5b9a\u57fa\u4e8e\u8fd9\u6837\u4e00\u4e2a\u4e8b\u5b9e\uff0c\u5373\u6700\u5927\u71b5\u5206\u5e03\u7b26\u5408\u6240\u6709\u786e\u5b9a\u6027\u5f71\u54cd\u7684\u7ed3\u679c\uff0c\u4f46\u9664\u6b64\u4e4b\u5916\uff0c\u5bf9\u5176\u5b83\u50cf\u7f3a\u5931\u4fe1\u606f\u8fd9\u6837\u7684\u5f71\u54cd\u4e0d\u7f6e\u53ef\u5426\u3002\u5f53\u4ee5\u71b5\u4f5c\u4e3a\u4e3b\u8981\u6982\u5ff5\u65f6\uff0c\u81ea\u7531\u80fd\u3001\u6982\u7387\u5206\u5e03\u51fd\u6570\u548cSFMs\u7b49\u76f8\u5173\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u5c31\u81ea\u7136\u5efa\u7acb\u8d77\u6765\u3002\u8fd9\u4e9b\u5173\u7cfb\u5728\u73b0\u5b9e\u4e16\u754c\u901a\u8fc7\u76f8\u5173\u6027\u8868\u8fbe\u5b83\u4eec\u81ea\u5df1\uff0c\u5728\u7269\u7406\u5c42\u9762\u4e0a\u901a\u8fc7\u6d4b\u91cf\u7cfb\u7edf\u72b6\u6001\u53d8\u91cf\u7684\u51fd\u6570\u4e5f\u662f\u53ef\u5f97\u7684\uff0c\u800c\u4e14\u539f\u5219\u4e0a\u5141\u8bb8\u5bf9\u7cfb\u7edf\u6240\u6709\u53c2\u6570\u8fdb\u884c\u7cfb\u7edf\u4f30\u8ba1\u3002<\/span><\/section>\n

<\/section>\n
2.1. \u9884\u6d4b\u7f16\u7801\u53ca\u5176\u5efa\u6a21\u6846\u67b6<\/strong><\/span><\/section>\n

<\/section>\n
\u9884\u6d4b\u7f16\u7801\u8ba8\u8bba\u7684\u5185\u5bb9\u53ca\u5176\u76f8\u5173\u6982\u5ff5\uff0c\u672c\u8d28\u4e0a\u57fa\u4e8e\u4e09\u4e2a\u6838\u5fc3\u65b9\u7a0b\uff1a<\/span><\/section>\n

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\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u5efa\u7acb\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u7b80\u5316\u5f62\u5f0f\uff0c\u4ee5\u6982\u7387\u5206\u5e03\u51fd\u6570p\u8fdb\u884c\u8868\u793a\uff0c\u5176\u4e2dp(x,y)\u662f\u72b6\u6001\u53d8\u91cfx\u548cy\u7684\u8054\u5408\u6982\u7387\uff0cp(y|x)\u662f\u7ed9\u5b9a\u53d8\u91cfx\u72b6\u6001\u7684\u6761\u4ef6\u4e0b\u53d8\u91cfy\u7684\u6761\u4ef6\u6982\u7387\u3002\u5728\u8d1d\u53f6\u65af\u6846\u67b6\u4e2d\uff0c\u53c2\u6570\u548c\u72b6\u6001\u53d8\u91cf\u5728\u4e00\u5b9a\u610f\u4e49\u4e0a\u5177\u6709\u76f8\u4f3c\u5730\u4f4d\uff0c\u5373\u5b83\u4eec\u90fd\u53ef\u4ee5\u7528\u5206\u5e03\u8fdb\u884c\u63cf\u8ff0\u5e76\u4e14\u4ee5\u53c2\u6570\u7684\u5f62\u5f0f\u8fdb\u5165\u6982\u7387\u51fd\u6570p\u4e2d\u3002\u4f8b\u5982\uff0c\u7ed9\u5b9a\u53c2\u6570k\uff0c\u72b6\u6001x\u548cy\u7684\u8054\u5408\u6982\u7387\u53ef\u88ab\u5199\u4e3ap(x,y|k)\uff0c\u786e\u5b9a\u4e86\u7ed9\u5b9a\u4e00\u7ec4\u53c2\u6570\u503ck\u7684\u6761\u4ef6\u4e0b\uff0c\u83b7\u5f97\u4e00\u7ec4\u6570\u636e (x,y)\u7684\u53ef\u80fd\u6027\uff0c\u5176\u4e2dk\u7684\u5148\u9a8c\u5206\u5e03\u4e3ap(k)\u3002\u5148\u9a8c\u4ee3\u8868\u6211\u4eec\u5bf9\u6a21\u578b\u548c\u521d\u59cb\u503c\u7684\u4e86\u89e3\u3002<\/span><\/section>\n

<\/section>\n
\u7b2c\u4e8c\u4e2a\u65b9\u7a0b\uff0c\u6717\u4e4b\u4e07\u65b9\u7a0b<\/span>\uff08\u6280\u672f\u4e0a\u5b58\u5728\u66f4\u7cbe\u786e\u7684\u5fae\u79ef\u5206\u5f62\u5f0f\u53ef\u4ee5\u5728\u4f8b\u5982[4]\u4e2d\u627e\u5230\uff0c\u6b64\u5904\u5047\u8bbe\u662f\u4f0a\u85e4\u5fae\u79ef\u5206\uff09<\/span>\u786e\u5b9a\u4e86\u751f\u6210\u6a21\u578b\uff0c\u5176\u4e2d\u795e\u7ecf\u6e90\u5c42\u9762\u7684\u5927\u8111\u6d3b\u52a8\u7531N\u7ef4\u72b6\u6001\u5411\u91cf Q=(x,y,…)\u2208RN<\/sup> \u8868\u793a\uff0cf(Q,k)\u4ee3\u8868\u786e\u5b9a\u6027\u5f71\u54cd\uff0c\u8868\u793a\u6210\u57fa\u4e8e\u72b6\u6001Q\u548c\u53c2\u6570k\uff08\u6216\u4e00\u7ec4\u53c2\u6570{k}\uff09\u7684M\u7ef4\u6d41\u5411\u91cff\u3002v\u2208RN<\/sup>\u786e\u5b9a\u4e86\u6da8\u843d\u5f71\u54cd\uff0c\u901a\u5e38\u5047\u8bbe\u4e3a <vi<\/sub>(t)vj<\/sub>(t’)>=c\u03b4ij<\/sub>\u03b4(t-t’) \u7684\u9ad8\u65af\u767d\u566a\u58f0\uff0c\u5176\u4e2d\u03b4ij<\/sub>\u662f Kronecker-delta \u51fd\u6570\uff0c\u03b4(t-t’)\u662fDirac\u51fd\u6570\u3002\u566a\u58f0\u5f71\u54cd<\/span>\uff08\u5305\u62ec\u4e58\u6027\u566a\u58f0\u6216\u6709\u8272\u566a\u58f0\uff09<\/span>\u53ef\u80fd\u6709\u66f4\u4e00\u822c\u7684\u516c\u5f0f\uff0c\u8bf7\u8bfb\u8005\u81ea\u884c\u67e5\u9605\u76f8\u5173\u6587\u732e\u3002<\/span><\/section>\n

<\/section>\n
\u7b2c\u4e09\u4e2a\u65b9\u7a0b\u786e\u7acb\u4e86\u89c2\u6d4b\u6a21\u578b\uff0c\u901a\u8fc7\u524d\u5411\u6a21\u578bh(Q)\u548c\u6d4b\u91cf\u566a\u58f0w\u5c06\u6e90\u6d3b\u52a8Q(t)\u4e0e\u5b9e\u9a8c\u83b7\u53d6\u7684\u4f20\u611f\u5668\u4fe1\u53f7Z(t)\u8054\u7cfb\u8d77\u6765\u3002\u5bf9\u4e8e\u8111\u7535\u56fe\u6d4b\u91cf\uff0ch\u662fMaxwell\u65b9\u7a0b\u786e\u5b9a\u7684\u589e\u76ca\u77e9\u9635\uff1b\u5bf9\u4e8e\u529f\u80fd\u78c1\u5171\u632f\u6210\u50cf\u6d4b\u91cf\uff0ch\u7531\u795e\u7ecf\u8840\u7ba1\u8026\u5408\u548c\u8840\u6d41\u52a8\u529b\u5b66\u7684Ballon\u2013Windkessel\u6a21\u578b\u7ed9\u51fa\u3002\u5728\u76ee\u524d\u7684\u60c5\u51b5\u4e0b\uff0c\u89c2\u6d4b\u6a21\u578b\u65e0\u5173\u7d27\u8981\uff0c\u4f46\u5728\u73b0\u5b9e\u4e16\u754c\u7684\u5e94\u7528\u4e2d\u975e\u5e38\u91cd\u8981\uff0c\u5e76\u4e14\u5728\u6a21\u578b\u53cd\u6f14\u548c\u53c2\u6570\u4f30\u8ba1\u95ee\u9898\u4e2d\u901a\u5e38\u662f\u4e3b\u8981\u7684\u6c61\u67d3\u56e0\u7d20\u3002\u51fa\u4e8e\u5b8c\u6574\u6027\u7684\u8003\u91cf\uff0c\u6211\u4eec\u6b64\u5904\u63d0\u53ca\u8fd9\u4e9b\u5de5\u7a0b\u95ee\u9898\uff0c\u4f46\u4e3a\u4e86\u7b80\u5355\u8d77\u89c1\uff0c\u5047\u8bbeh\u662f\u6d4b\u91cf\u566a\u58f0\u4e3a\u96f6\u7684\u6052\u7b49\u8fd0\u7b97\uff0c\u56e0\u6b64Z=Q\u3002<\/span><\/section>\n

<\/section>\n
\u9884\u6d4b\u7f16\u7801\u6d89\u53ca\u884c\u4e3a\u795e\u7ecf\u79d1\u5b66\u4e2d\u4e00\u5927\u7814\u7a76\u9886\u57df[21\uff0c22]\uff0c\u7279\u522b\u662f\u81f4\u529b\u4e8e\u611f\u77e5-\u884c\u52a8\u548c\u52a8\u529b\u7cfb\u7edf\u7814\u7a76\u7684\u751f\u6001\u5fc3\u7406\u5b66<\/span>\uff08ecological psychology\uff09<\/span>[23\uff0c24]\u3002\u5728\u8fd9\uff0cJames J Gibson \u5f3a\u8c03\u73af\u5883\u7684\u91cd\u8981\u6027[25]\uff0c\u5c24\u5176\u662f\u6709\u673a\u4f53\u6240\u5904\u7684\u73af\u5883\u5982\u4f55\u4e3a\u5176\u63d0\u4f9b\u5404\u79cd\u884c\u4e3a\u7684\u611f\u77e5\u3002\u8fd9\u79cd\u611f\u77e5-\u884c\u52a8\u5faa\u73af\u4e0e\u9884\u6d4b\u7f16\u7801\u4e2d\u5185\u90e8\u751f\u6210\u6a21\u578b\u7684\u9884\u6d4b\u548c\u66f4\u65b0\u5faa\u73af\u5bc6\u5207\u5339\u914d\u3002\u4f46\u751f\u6001\u5fc3\u7406\u5b66\u5f3a\u8c03\u6709\u4e00\u4e2a\u7ec6\u5fae\u5dee\u522b\uff0c\u5373\u751f\u6001\u5b66\u4e0a\u53ef\u83b7\u5f97\u7684\u4fe1\u606f\u2014\u2014\u76f8\u5bf9\u4e8e\u5916\u56f4\u6216\u5185\u90e8\u611f\u89c9\u2014\u2014\u5bfc\u81f4\u611f\u77e5-\u884c\u52a8\u52a8\u529b\u5b66\u7684\u51fa\u73b0\u3002Scott Kelso\u53ca\u5176\u540c\u4e8b\u4e3a\u8be5\u6846\u67b6\u7684\u5f62\u5f0f\u5316\u505a\u51fa\u5de8\u5927\u8d21\u732e\uff0c\u5e76\u5f00\u53d1\u4e86\u5b9e\u9a8c\u8303\u5f0f\uff0c\u7528\u4ee5\u6d4b\u8bd5\u751f\u7269\u4f53\u548c\u73af\u5883\u4e4b\u95f4\u534f\u8c03\u7684\u5185\u90e8\u6a21\u578b\u7684\u52a8\u529b\u5b66\u7279\u6027[26-28]\u3002\u8fd9\u4e9b\u8303\u5f0f\u7406\u8bba\u4e0a\u53d7Hermann Haken\u534f\u540c\u5b66[4]\u7684\u542f\u53d1\uff0c\u800c\u534f\u540c\u5b66\u4e00\u76f4\u662f\u81ea\u7ec4\u7ec7\u7406\u8bba\u7684\u57fa\u7840\u3002\u8fd9\u5f15\u53d1\u4e86\u5927\u91cf\u91cd\u70b9\u5173\u6ce8\u611f\u77e5\u548c\u884c\u52a8\u72b6\u6001\u4e4b\u95f4\u8f6c\u6362\u7684\u7814\u7a76\u5de5\u4f5c\uff0c\u5305\u62ec\u53cc\u611f\u89c9\u548c\u591a\u611f\u89c9\u8fd0\u52a8\u534f\u8c03\u7684\u5efa\u6a21[29-32]\u548c\u7cfb\u7edf\u5b9e\u9a8c\u6d4b\u8bd5[33-44]\u3002\u8fd9\u4e9b\u65b9\u6cd5\u4e4b\u540e\u63a8\u5e7f\u5230\u66f4\u5927\u8303\u56f4\u7684\u8303\u5f0f\u4e2d[45-53]\uff0c\u65e8\u5728\u63d0\u53d6\u751f\u7269\u4f53\u548c\u73af\u5883\u7684\u4ea4\u4e92\u884c\u4e3a\u7684\u4e3b\u8981\u7279\u5f81[22]\u3002\u4f17\u591a\u5de5\u4f5c\u4ea7\u751f\u7684\u5b9e\u8d28\u6027\u8bc1\u636e\u6709\u5229\u4e8e\u884c\u4e3a\u7684\u52a8\u6001\u63cf\u8ff0\uff0c\u8fd9\u4e9b\u8bc1\u636e\u53ef\u4ee5\u5f52\u5165SFMs\u6846\u67b6\uff0c\u7528\u4e8e\u884c\u4e3a[48]\u548c\u5927\u8111[54-56]\u4e2d\u529f\u80fd\u611f\u77e5-\u884c\u52a8\u53d8\u91cf\u3002<\/span><\/section>\n

<\/section>\n
2.2. \u6700\u5927\u4fe1\u606f\u539f\u7406<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u6211\u4eec\u901a\u8fc7\u8ba1\u7b97\u5bf9\u5e94\u7684\u6982\u7387\u5206\u5e03pi<\/sub>\uff0c\u4ece\u800c\u7406\u89e3\u51b3\u5b9a\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u8fc7\u7a0b\uff0c\u8be5\u8fc7\u7a0b\u51b3\u5b9a\u4e86\u72b6\u6001\u53d8\u91cfx\u7684\u79bb\u6563\u503c xi<\/sub>\u3002\u9999\u519c\u8bc1\u660e\u8fd9\u6837\u4e00\u4e2a\u663e\u8457\u4e8b\u5b9e\uff0c\u5373\u5b58\u5728\u4e00\u4e2a\u4fe1\u606f\u91cf H(p1<\/sub>,…pn<\/sub>)\uff0c\u53ef\u4ee5\u552f\u4e00\u6d4b\u5ea6\u7531\u8fd9\u4e9b\u6982\u7387\u5206\u5e03\u6240\u8868\u8fbe\u7684\u4e0d\u786e\u5b9a\u6027[8]\u3002\u4ed6\u5728\u6700\u521d\u7684\u8bc1\u660e\u4e2d\u6307\u51fa\uff0c\u4e09\u5927\u57fa\u672c\u6761\u4ef6\u7684\u8981\u6c42\uff0c\u5c24\u5176\u662f\u4e8b\u4ef6\u548c\u6982\u7387\u7ec4\u5408\u5b9a\u5f8b\uff0c\u81ea\u7136\u5f62\u6210\u5982\u4e0b\u8868\u8fbe\u5f0f\u3002<\/span><\/section>\n

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\u5728\u8fd9\u91cc\uff0cK\u662f\u4e00\u4e2a\u6b63\u7684\u5e38\u6570\u3002\u6d4b\u5ea6H\u76f4\u63a5\u5bf9\u5e94\u4e8e\u7edf\u8ba1\u529b\u5b66\u4e2d\u71b5\u7684\u8868\u8fbe\u5f0f\uff0c\u79f0\u4e3a\u4fe1\u606f\u71b5[7]\u3002\u5bf9\u5176\u5c5e\u6027\u7684\u8ba8\u8bba\u901a\u5e38\u4ece\u89c2\u5bdf\u8005\u53ef\u83b7\u5f97\u4fe1\u606f\u91cf\u76f8\u5173\u7684\u8be6\u5c3d\u6982\u7387\u8fd9\u4e00\u89d2\u5ea6\u8fdb\u884c\u5c55\u5f00\u3002\u5728\u6ca1\u6709\u4efb\u4f55\u533a\u522b\u4fe1\u606f\u7684\u60c5\u51b5\u4e0b\uff0c\u62c9\u666e\u62c9\u65af\u4e0d\u5145\u5206\u7406\u7531\u539f\u5219<\/span>\uff08principle of insufficient reason\uff09<\/span>\u7ed9\u4e24\u4e2a\u4e8b\u4ef6\u5206\u914d\u540c\u7b49\u6982\u7387\u3002\u8be5\u4e3b\u89c2\u601d\u60f3\u5b66\u6d3e\u8ba4\u4e3a\u6982\u7387\u662f\u4eba\u7c7b\u65e0\u77e5\u7684\u8868\u73b0\uff0c\u8868\u8fbe\u4e86\u6211\u4eec\u5bf9\u4e8b\u4ef6\u662f\u5426\u53d1\u751f\u7684\u671f\u671b\u3002\u8fd9\u79cd\u601d\u60f3\u662f\u9884\u6d4b\u7f16\u7801\u7406\u8bba\u53ca\u5176\u89e3\u91ca\u5927\u8111\u4ea7\u751f\u8ba4\u77e5\u8fc7\u7a0b\u7684\u57fa\u7840\u3002\u5ba2\u89c2\u601d\u60f3\u5b66\u6d3e\u6839\u690d\u4e8e\u7269\u7406\u5b66\uff0c\u8ba4\u4e3a\u6982\u7387\u662f\u4e8b\u4ef6\u7684\u5ba2\u89c2\u5c5e\u6027\uff0c\u539f\u5219\u4e0a\u8be5\u5c5e\u6027\u603b\u80fd\u7531\u968f\u673a\u5b9e\u9a8c\u4e2d\u4e8b\u4ef6\u7684\u9891\u7387\u6765\u6d4b\u5ea6\u3002\u5728\u8fd9\uff0c\u901a\u8fc7\u7814\u7a76\u9884\u6d4b\u7f16\u7801\u4e0b\u7684\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u8fc7\u7a0b\uff0c\u6211\u4eec\u5e0c\u671b\u5728\u8fd9\u4e00\u70b9\u4e0a\u4fdd\u6301\u4e2d\u7acb\u3002\u5bf9\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u4f5c\u7528\u7684\u63d0\u53ca\u901a\u5e38\u5c5e\u4e8e\u5ba2\u89c2\u5b66\u6d3e\u7684\u8bed\u8a00\uff0c\u5176\u4e2d\uff0c\u9884\u6d4b\u7f16\u7801\u6846\u67b6\u5185\u7684\u540e\u7eed\u89e3\u91ca\u5219\u662f\u4e3b\u89c2\u5b66\u6d3e\u7684\u4e00\u90e8\u5206\u3002\u9884\u6d4b\u7f16\u7801\u4e2d\u7684\u751f\u6210\u6a21\u578b\u901a\u8fc7\u6717\u4e4b\u4e07\u65b9\u7a0b\u8868\u793a\u4e24\u79cd\u7c7b\u578b\u7684\u4f5c\u7528\u5e76\u5f62\u6210\u6982\u7387\u51fd\u6570\uff0c\u5982\u6b64\uff0c\u901a\u8fc7\u7ecf\u9a8c\u6d4b\u5ea6\u51fd\u6570<g(x)>\uff0c\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u83b7\u53d6\u8fd9\u4e00\u4fe1\u606f\u7684\u9014\u5f84\u3002\u5176\u4e2d\uff0c\u5c16\u62ec\u53f7\u8868\u793a\u671f\u671b\u503c\u3002<\/span><\/section>\n

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g(x)\u95f4\u7684\u76f8\u5173\u6027\u4ee5\u53ca\u5f52\u4e00\u5316\u8981\u6c42\u03a3i<\/sub>pi<\/sub>=1\uff0c\u8868\u8fbe\u4e86\u7531\u786e\u5b9a\u6027\u548c\u968f\u673a\u6027\u5f71\u54cd\u5e26\u6765\u7684\u7ea6\u675f\uff0c\u5728\u8fd9\u4e9b\u7ea6\u675f\u4e0b\u4fe1\u606f\u71b5\u5b58\u5728\u6700\u5927\u503c\u3002\u9664\u4f7f\u4fe1\u606f\u71b5\u6700\u5927\u7684\u8d4b\u503c\u5916\uff0c\u4efb\u4f55\u5176\u5b83\u7684\u8d4b\u503c\u90fd\u4f1a\u5f15\u5165\u5176\u5b83\u786e\u5b9a\u6027\u7684\u504f\u5dee\u6216\u4efb\u610f\u5047\u8bbe\uff0c\u800c\u6211\u4eec\u5e76\u672a\u505a\u8fd9\u4e9b\u5047\u8bbe\u3002\u8fd9\u79cd\u6d1e\u89c1\u662fEdwin T Jaynes\u6700\u5927\u4fe1\u606f\u51c6\u5219\u7684\u672c\u8d28[7]\u3002\u56e0\u6b64\uff0c\u91c7\u7528\u7ecf\u5178\u529b\u5b66\u4e2d\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u5f15\u5165Lagrange\u53c2\u6570\u03bbi<\/sub>\uff0c\u6211\u4eec\u6700\u5927\u5316\u4fe1\u606f\u71b5H\u7136\u540e\u5f97\u5230\u4e0b\u9762\u516c\u5f0f\uff1a<\/span><\/section>\n

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\u5176\u4e2d\u6982\u7387\u5206\u5e03\u8868\u8fbe\u5f0f\u4e00\u822c\u5316\u4e3a\u4e8b\u4ef6xi<\/sub>\u7684\u591a\u6d4b\u5ea6\u51fd\u6570gi<\/sub>(xi<\/sub>)\u3002\u8be5\u5206\u5e03\u7684\u71b5S\u6700\u5927\u5316\uff0c\u8bb0\u4e3a\uff1a<\/span><\/section>\n


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\u8054\u7cfb\u5982\u4e0b\uff1a<\/span><\/section>\n

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3. \u81ea\u7ec4\u7ec7\u7cfb\u7edf\u4e2d\u7684\u6d8c\u73b0<\/span><\/strong><\/strong><\/p>\n

\u2014\u2014\u7cfb\u7edf\u52a8\u529b\u5b66\u5efa\u6a21<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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\u867d\u7136\u4e0a\u8ff0\u611f\u77e5-\u884c\u52a8\u52a8\u529b\u5b66\u6846\u67b6\u548c\u9884\u6d4b\u7f16\u7801\u4e92\u8865\u5730\u89e3\u91ca\u4e86\u5927\u8111\u548c\u884c\u4e3a\u5982\u4f55\u901a\u8fc7\u4f5c\u7528\u4e8e\u73af\u5883\u4ee5\u53ca\u89c2\u5bdf\u73af\u5883\u548c\u81ea\u6211\u8fdb\u884c\u5851\u9020\uff0c\u4f46\u662fSFMs\u6846\u67b6\u7ed9\u51fa\u4e86\u8fd9\u4e9b\u5f62\u6210\u8fc7\u7a0b\u7684\u6700\u7ec8\u7ed3\u679c\u5982\u4f55\u4f53\u73b0\u7684\u673a\u68b0\u56fe\u3002\u540e\u8005\u4ee5\u534f\u8c03\u7684\u795e\u7ecf\u6d3b\u52a8\u81ea\u53d1\u5730\u6d8c\u73b0\u51fa\u6d41\u5f62\u7684\u5f62\u5f0f\uff0c\u4e3a\u6301\u7eed\u6f14\u5316\u7684\u5185\u90e8\u751f\u6210\u6a21\u578b\u63d0\u4f9b\u4e86\u62bd\u8c61\u76f8\u7a7a\u95f4\u4e2d\u65f6\u7a7a\u7ed3\u6784\u7684\u6982\u5ff5\u5316\uff0c\u5927\u8111\u4fbf\u5728\u8fd9\u4e9b\u6d41\u5f62\u4e0a\u4f53\u9a8c\u548c\u6539\u9020\u4e16\u754c\u3002\u73b0\u5728\u6211\u4eec\u7b80\u8981\u8ba8\u8bba\u5728\u5927\u8111\u52a8\u529b\u5b66\u80cc\u666f\u4e0bSFMs\u7814\u7a76\u4e2d\u7684\u6838\u5fc3\u52a8\u529b\u7cfb\u7edf\u6982\u5ff5\u4ee5\u53ca\u76f8\u5173\u7684\u6570\u5b66\u673a\u5236\u3002<\/span><\/section>\n

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3.1. \u65f6\u95f4\u5c3a\u5ea6\u5206\u79bb<\/span><\/strong><\/span><\/section>\n

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3.2. \u534f\u540c\u5b66<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u9996\u5148\u6211\u4eec\u6982\u8ff0\u534f\u540c\u5b66\u4e2d\u7684\u4e00\u4e9b\u6982\u5ff5\uff0c\u8fd9\u6709\u52a9\u4e8e\u66f4\u597d\u5730\u7406\u89e3SFMs\u6982\u5ff5\u3002\u534f\u540c\u5b66\u662f\u8fdc\u79bb\u70ed\u5e73\u8861\u7684\u5f00\u653e\u7cfb\u7edf<\/strong><\/span>\uff08\u5373\u90a3\u4e9b\u901a\u8fc7\u7269\u8d28\u3001\u80fd\u91cf\u548c\/\u6216\u4fe1\u606f\u901a\u91cf\u4e0e\u73af\u5883\u76f8\u8054\u7cfb\u7684\u7cfb\u7edf\uff09<\/span>\u4e2d\u81ea\u7ec4\u7ec7\u6a21\u5f0f\u5f62\u6210\u7684\u7406\u8bba\uff0c\u800c\u8fd9\u4e9b\u7cfb\u7edf\u7531\u65e0\u6570\u5177\u6709\u5f31\u76f8\u4e92\u4f5c\u7528\u7684\u5fae\u89c2\u5143\u7d20\u7ec4\u6210<\/strong>[4]\u3002\u7531\u4e8e\u5fae\u89c2\u5143\u7d20\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u79cd\u7cfb\u7edf\u53ef\u80fd\u5728\u7a7a\u95f4\u4e0a\u53d8\u5f97\u6709\u6761\u7406\uff08\u6709\u5e8f\uff09\u548c\u65f6\u95f4\u4e0a\u53d8\u6210\u6709\u5e8f\u6a21\u5f0f<\/strong>\uff0c\u8fd9\u901a\u5e38\u5728\u672c\u8d28\u4e0a\u662f\u5b8f\u89c2\u7684\uff0c\u4e14\u53ef\u4ee5\u7528\u6709\u9650\u7684\u6240\u8c13\u5e8f\u53c2\u91cf<\/span>\uff08\u6216\u96c6\u5408\u53d8\u91cf\uff09<\/span>\u6765\u63cf\u8ff0\u3002\u5927\u8111\u6d3b\u52a8\u7684\u4e00\u4e2a\u5b8f\u89c2\u6a21\u5f0f\u5931\u53bb\u7a33\u5b9a\u6027\u800c\u53e6\u4e00\u4e2a\u6a21\u5f0f\u5360\u636e\u4e0a\u98ce\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u8111\u6d3b\u52a8\u6a21\u5f0f\u7684\u81ea\u53d1\u8f6c\u6362<\/span>\uff08\u5373\u975e\u5e73\u8861\u76f8\u53d8\uff09<\/span>\u3002\u7cfb\u7edf\u72b6\u6001<\/span>\uff08\u6216\u76f8\uff09<\/span>\u7684\u7a33\u5b9a\u6027\u662f\u6307\uff0c\u5982\u679c\u6270\u52a8\u4f7f\u5176\u8fdc\u79bb\uff0c\u5b83\u5c06\u503e\u5411\u4e8e\u8fd4\u56de\u90a3\u4e2a\u7a33\u6001\u3002\u5982\u679c\u5931\u53bb\u7a33\u5b9a\u6027\uff0c\u7cfb\u7edf\u53cd\u800c\u4f1a\u8d8b\u5411\u4e8e\u8fdc\u79bb\u90a3\u4e2a\u72b6\u6001\uff0c\u800c\u8f6c\u5411\u53e6\u4e00\u4e2a\u7a33\u6001\u3002\u63a5\u8fd1\u8fd9\u4e9b<\/span>\uff08\u5b8f\u89c2\uff09<\/span>\u4e0d\u7a33\u5b9a\u70b9\u65f6\uff0c\u8fd4\u56de\u7684\u65f6\u95f4\u5c06\u5927\u5927\u589e\u52a0\u3002\u56e0\u6b64\uff0c\u5b8f\u89c2\u72b6\u6001\u5bf9\u6270\u52a8\u7684\u53cd\u5e94\u6f14\u5316\u5f97\u76f8\u5f53\u7f13\u6162\uff0c\u800c\u5176\u5e95\u5c42\u7684\u5fae\u89c2\u5143\u7d20\u5219\u4fdd\u6301\u5404\u81ea\u7684\u65f6\u95f4\u5c3a\u5ea6\u3002\u9020\u6210\u7684\u7ed3\u679c\u662f\uff0c\u5b83\u4eec\u52a8\u529b\u5b66\u7684\u65f6\u95f4\u5c3a\u5ea6\u5dee\u5f02\u5de8\u5927<\/span>\uff08\u5373\u65f6\u95f4\u5c3a\u5ea6\u5206\u79bb\uff09<\/span>\u3002\u4ece\u7f13\u6162\u6f14\u5316\u7684\u5b8f\u89c2\u72b6\u6001\u89c6\u89d2\u6765\u770b\uff0c\u5fae\u89c2\u5143\u7d20\u53d8\u5316\u5982\u6b64\u4e4b\u5feb\u4ee5\u81f3\u4e8e\u5b83\u4eec\u53ef\u4ee5\u5373\u523b\u9002\u5e94\u5b8f\u89c2\u53d8\u5316\u3002\u56e0\u6b64\uff0c\u5c3d\u7ba1\u5b8f\u89c2\u6a21\u5f0f\u7531\u5b50\u7cfb\u7edf\u4ea7\u751f\uff0c\u4f46\u662f\uff0c\u6253\u6bd4\u65b9\u8bf4\uff0c\u524d\u8005\u5f79\u4f7f\u540e\u8005[4]\u3002\u6709\u5e8f\u72b6\u6001\u603b\u662f\u53ef\u4ee5\u7531\u5c11\u6570\u51e0\u4e2a\u53d8\u91cf\u6765\u63cf\u8ff0<\/span>\uff08\u81f3\u5c11\u5728\u5206\u5c94\u9644\u8fd1\u662f\u5982\u6b64\uff09<\/span>\uff0c\u56e0\u6b64\uff0c\u6700\u521d\u7684\u9ad8\u7ef4\u7cfb\u7edf\u7684\u72b6\u6001\u53ef\u4ee5\u7531\u51e0\u4e2a\u751a\u81f3\u5355\u4e2a\u96c6\u5408\u53d8\u91cf\u6765\u6982\u62ec\uff0c\u5373\u5e8f\u53c2\u91cf\u3002\u8be5\u5e8f\u53c2\u91cf\u5f20\u6210\u5de5\u4f5c\u7a7a\u95f4\u3002\u5f79\u4f7f\u5e8f\u53c2\u91cf\u548c\u88ab\u5f79\u4f7f\u7684\u751f\u6210\u5e8f\u53c2\u91cf\u7684\u5fae\u89c2\u5143\u7d20\u4e4b\u95f4\u7684\u5faa\u73af\u5173\u7cfb\u6709\u65f6\u4e5f\u88ab\u79f0\u4e3a\u5faa\u73af\u56e0\u679c<\/span>\uff08circular causality\uff09<\/span>\uff0c\u8fd9\u5b9e\u9645\u4e0a\u5141\u8bb8\u4e86\u5bf9\u7cfb\u7edf\u52a8\u529b\u5b66\u6027\u8d28\u8fdb\u884c\u4f4e\u7ef4\u63cf\u8ff0[57]\u3002\u5faa\u73af\u56e0\u679c\u7684\u6982\u5ff5\u548c\u81ea\u7ec4\u7ec7\u7cfb\u7edf\u4e2d\u4f4e\u7ef4\u52a8\u529b\u5b66\u7684\u6d8c\u73b0\u662fHermann Haken\u534f\u540c\u5b66\u7684\u6838\u5fc3[4]\u3002<\/span><\/section>\n

<\/section>\n
\u534f\u540c\u5b66\u7684\u6570\u5b66\u5f62\u5f0f\u7b80\u8ff0\u5982\u4e0b\u3002N\u7ef4\u72b6\u6001\u5411\u91cfQ(t)\u2208RN<\/sup>\u5b9a\u4e49\u4e3a\u65f6\u95f4\u51fd\u6570\uff0c\u4e14\u5305\u542b\u4e86\u7cfb\u7edf\u7684\u6240\u6709\u72b6\u6001\u53d8\u91cf\u3002\u72b6\u6001\u5411\u91cf\u7684\u6f14\u5316\u7531\u975e\u7ebf\u6027\u5e38\u5fae\u5206\u65b9\u7a0b\u523b\u753b\uff1a<\/span><\/section>\n

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<\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\uff0cF\u8868\u793a\u523b\u753b\u4e86\u6240\u6709\u4ea4\u4e92\u4f5c\u7528\u7684\u975e\u7ebf\u6027\u51fd\u6570\uff0c{k}\u8868\u793a\u63a7\u5236\u53c2\u6570\u96c6\uff0c\u63a7\u5236\u7cfb\u7edf\u7684\u72b6\u6001\u5e76\u4e14\u5177\u6709\u65f6\u95f4\u72ec\u7acb\u6027\u3002\u975e\u7ebf\u6027\u6f14\u5316\u65b9\u7a0b\u5305\u542b\u566a\u58f0\u03c5(t)\u7684\u5f71\u54cd\uff0c\u8fd9\u5728\u4e4b\u540e\u4f1a\u8003\u8651\uff0c\u4f46\u975e\u73b0\u5728\u3002\u72b6\u6001\u5411\u91cf\u53ca\u5176\u6f14\u5316\u65b9\u7a0b\u4e5f\u53ef\u8fdb\u884c\u6269\u5c55\uff0c\u4ee5\u4f53\u73b0\u72b6\u6001\u53d8\u91cf\u7684\u7a7a\u95f4\u4f9d\u8d56\u6027\uff0c\u4f46\u6b64\u5904\u4ec5\u8003\u8651\u7a7a\u95f4\u79bb\u6563\u7cfb\u7edf\u5c31\u5df2\u8db3\u591f\u4e86\u3002\u8be6\u7ec6\u7684\u6570\u5b66\u65b9\u6cd5\u89c1 Haken<\/span> (1983)<\/span>\u3002<\/span>
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\u534f\u540c\u5b66\u4e2d\u81ea\u7ec4\u7ec7\u548c\u6d8c\u73b0\u7684\u5207\u5165\u70b9\u662f\u5b8f\u89c2\u5c42\u9762\u7cfb\u7edf\u72b6\u6001\u7684\u8d28\u53d8<\/span>\uff08\u72b6\u6001\u8f6c\u6362\uff09<\/span>\u3002\u4e00\u4e2a\u7ed9\u5b9a\u7684\u72b6\u6001\u901a\u5e38\u5bf9\u5e94\u4e8e\u72b6\u6001\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a<\/span>\uff08\u7a33\u5b9a\uff09<\/span>\u4e0d\u52a8\u70b9\u6216\u5468\u671f<\/span>\uff08\u6781\u9650\uff09<\/span>\u73af<\/span>\uff08\u89c1\u56fe2\uff09<\/span>\uff0c\u534f\u540c\u5b66\u65e8\u5728\u63cf\u8ff0\u72b6\u6001\u7a7a\u95f4\u4e2d\u5176\u5c40\u90e8\u9644\u8fd1\u7684\u6d41<\/span>\uff08\u89c1\u56fe3\uff09<\/span>\u3002<\/span><\/section>\n

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  <\/span><\/section>\n

\u56fe3\uff1a\u534f\u540c\u5b66\u548cSFMs\u3002\u5728\u81ea\u7ec4\u7ec7\u4e2d\uff0c\u6d8c\u73b0\u6a21\u5f0f\u88ab\u9650\u5236\u5728\u4f4e\u7ef4\u6d41\u5f62\u4e2d\uff0c\u5982\u7403\u9762\u3002\u5f53\u6d41\u5c40\u90e8\u6539\u53d8\u5176\u62d3\u6251\u65f6\uff08\u5de6\u4fa7\u65b9\u5f62\u533a\u57df\uff09\uff0c\u534f\u540c\u5b66\u7684\u4e34\u754c\u72b6\u6001\u51fa\u73b0\u3002\u800cSFMs\u7684\u4e34\u754c\u72b6\u6001\u662f\u975e\u5c40\u57df\u7684\uff0c\u5f53\u6574\u4e2a\u6d41\u5f62\u7684\u6d41\u4e3a\u96f6\u65f6\u51fa\u73b0\uff08\u4e34\u754c\u72b6\u6001\uff09\u3002<\/span><\/p>\n


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\u4e0e\u7a33\u6001Q0<\/sub>\u7684\u504f\u5dee\u03b5(t)\u4e3aQ(t)=Q0<\/sub>+\u03b5(t)\uff0c\u5176\u65f6\u95f4\u6f14\u5316\u53ef\u4ee5\u7528F\u5728\u7a33\u6001Q0<\/sub>\u9644\u8fd1\u7684\u6cf0\u52d2\u5c55\u5f00\u5f0f\u6765\u8fd1\u4f3c\uff1a<\/span><\/section>\n

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\u5176\u4e2dL(Q0<\/sub>,{k})\u548cA(Q0<\/sub>,{k})\u5206\u522b\u662f\u6cf0\u52d2\u5c55\u5f00\u5f0f\u7684\u4e00\u9636\u9879\u548c\u4e8c\u9636\u9879\u3002\u968f\u7740\u63a7\u5236\u53c2\u6570{k}\u7684\u53d8\u5316\uff0c\u5f15\u5bfc\u7cfb\u7edf\u901a\u8fc7\u53c2\u6570\u7a7a\u95f4\uff0c\u9047\u5230\u5bfc\u81f4\u5206\u53c9\u7684\u53c2\u6570\u914d\u7f6e\uff0c\u81f4\u4f7f\u5f53\u524d\u72b6\u6001\u7684\u7a33\u5b9a\u6027\u53d1\u751f\u53d8\u5316\uff0c\u5bfc\u81f4\u7cfb\u7edf\u5728\u5b8f\u89c2\u5c42\u9762\u4e0a\u4ea7\u751f\u91cd\u5927\u91cd\u7ec4\u3002\u5206\u53c9\u70b9\u5b9a\u4e49\u4e86\u5de5\u4f5c\u70b9k0<\/sub>\uff0c\u56e0\u6b64\u7ee7\u72b6\u6001\u7a7a\u95f4\u5de5\u4f5c\u70b9Q0<\/sub>\u4e4b\u540e\uff0c\u5728\u53c2\u6570\u7a7a\u95f4\u4e2d\u5f62\u6210\u7b2c\u4e8c\u4e2a\u5c40\u90e8\u7ea6\u675f\u3002\u5728\u8fd9\u4e9b\u5c40\u90e8\u60c5\u51b5\u4e0b\uff0c\u96c5\u53ef\u6bd4\u77e9\u9635L(Q0<\/sub>,{k0<\/sub>})\u7684\u7279\u5f81\u503c\u03bb0<\/sub>\u81f3\u5c11\u6709\u4e00\u4e2a\u53d8\u4e3a\u96f6\uff0c\u5141\u8bb8\u5e94\u7528\u5c40\u90e8\u4e2d\u5fc3\u6d41\u5f62\u5b9a\u7406\u3002\u8fd9\u8868\u660e\uff0c\u65b0\u53d8\u91cf\u7684\u5c0f\u5b50\u96c6Q(t)\u2208RM<\/sup>\uff0cM<<N\uff0c\u5373\u5e8f\u53c2\u91cf\u51fa\u73b0\uff0c\u5e76\u901a\u8fc7\u65f6\u95f4\u5c3a\u5ea6\u5206\u79bb\u7684\u65b9\u5f0f\u4e3b\u5bfc\u7740\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\uff0c\u4ee5\u53ca\u5f79\u4f7f\u5269\u4f59\u53d8\u91cf s(t)\u2208R(N-M)<\/sup> \uff0c\u5176\u4e2d\uff0c\u5e8f\u53c2\u91cfq(t)\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\u7f13\u6162\u800c\u88ab\u5f79\u4f7f\u53d8\u91cfs(t)\u5219\u8fc5\u901f\u3002\u5728\u534f\u540c\u5b66\u672f\u8bed\u4e2d\uff0c\u5f79\u4f7f<\/span>\uff08enslaving\uff09<\/span>\u662f\u6307\u53d8\u91cfs(t)\u7684\u5185\u5728\u52a8\u529b\u5b66\u53ef\u4ee5\u88ab\u9694\u7edd\u6d88\u9664\uff0c\u5176\u957f\u671f\u6f14\u5316\u53ef\u4ee5\u8868\u793a\u4e3a\u5e8f\u53c2\u91cf\u51fd\u6570\uff0c\u5373s(t)=s(q(t))\u3002\u8fd9\u4fbf\u5f15\u51fa\u6d8c\u73b0\u52a8\u529b\u5b66\u7684\u7b80\u5316\u63cf\u8ff0\uff1a<\/span><\/section>\n

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\u5176\u4e2dP\u662f\u53c2\u6570\u4e3a{k}\u548cQ0<\/sub>\u7684\u975e\u7ebf\u6027\u51fd\u6570\uff0c\u4e14\u53ef\u901a\u8fc7\u5206\u89e3F\u4e3a\u5e8f\u53c2\u91cf\u548c\u5f79\u4f7f\u53d8\u91cf\u8fdb\u884c\u89e3\u6790\u8ba1\u7b97\u3002<\/span><\/section>\n

<\/section>\n
3.3. \u6d41\u5f62\u4e2d\u7ed3\u6784\u5316\u6d41\u6e90\u4e8e\u5bf9\u79f0\u6027\u7834\u7f3a<\/strong><\/span><\/section>\n

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4.1. \u795e\u7ecf\u7fa4\u4f53\u6a21\u578b\u663e\u793a\u51fa\u57fa\u672c\u76842D\u52a8\u529b\u5b66<\/strong><\/span><\/section>\n

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\u795e\u7ecf\u7fa4\u4f53\u6a21\u578b<\/span>\uff08neural mass model\uff09<\/span>\u662f\u795e\u7ecf\u5143\u96c6\u4f53\u6d3b\u52a8\u7684\u7b80\u5316\u6570\u5b66\u8868\u793a\u3002\u5b83\u901a\u5e38\u6765\u6e90\u4e8e\u7531\u8026\u5408\u70b9\u795e\u7ecf\u5143\u6a21\u578b\u8868\u793a\u7684\u4e00\u7fa4\u795e\u7ecf\u5143\u3002\u5728\u5bf9\u52a8\u4f5c\u7535\u4f4d\u5206\u5e03\u548c\/\u6216\u795e\u7ecf\u5143\u95f4\u8026\u5408\u7684\u7edf\u8ba1\u5047\u8bbe\u4e0b\uff0c\u5e94\u7528\u5e73\u5747\u573a\u7406\u8bba\u63a8\u5bfc\u96c6\u4f53\u53d8\u91cf\u65b9\u7a0b\uff0c\u523b\u753b\u795e\u7ecf\u5143\u7fa4\u7684\u5747\u503c\u3001\u65b9\u5dee\u548c\u66f4\u9ad8\u7edf\u8ba1\u77e9\u7684\u6f14\u5316\u3002\u663e\u8457\u7684\u4f8b\u5b50\u5305\u62ec\u5047\u8bbe\u6cca\u677e\u5206\u5e03\u5c16\u5cf0\u7684Brunel Wang\u6a21\u578b[63]\uff0cZerlaut\u7b49\u4eba\u7684\u4f7f\u7528\u4e3b\u65b9\u7a0b\u548c\u4f20\u9012\u51fd\u6570\u5f62\u5f0f\u7684\u6a21\u578b[64]\uff0c\u4ee5\u53ca\u5229\u7528\u5bfc\u81f4\u795e\u7ecf\u5143\u540c\u6b65\u96c6\u7fa4\u7684\u795e\u7ecf\u5143\u53c2\u6570\u5f02\u8d28\u6027\u8fdb\u884c\u8bbe\u8ba1\u7684Stefanescu\u2013Jirsa\u6a21\u578b[65\uff0c66]\u3002\u56e0\u4e3a\u662f\u5728Lorentzian\u5047\u8bbe\u4e0b\u7684\u4e25\u5bc6\u8bba\u8bc1\uff0cMontbrio\u7b49\u4eba\u7684\u5e73\u5747\u573a\u63a8\u5bfc\u4ece\u7406\u8bba\u89d2\u5ea6\u770b\u6781\u5177\u5438\u5f15\u529b[67]\u3002\u5b83\u5bfc\u51fa\u4e86\u4e24\u4e2a\u96c6\u4f53\u72b6\u6001\u53d8\u91cf\uff0c\u5373\u5e73\u5747\u653e\u7535\u7387r\u548c\u5e73\u5747\u795e\u7ecf\u5143\u819c\u7535\u4f4d V\u3002\u76f8\u5e94\u7684\u76f8\u6d41\u548c\u65b9\u7a0b\u5206\u522b\u89c1\u56fe5A\u548c5B\u3002\u8fd9\u4e9b\u4ee5\u53ca\u5176\u4ed6\u6240\u6709\u795e\u7ecf\u7fa4\u4f53\u6a21\u578b\u7684\u5171\u540c\u70b9\u662f\uff0c\u5c06\u5e73\u5747\u573a\u52a8\u529b\u5b66\u7b80\u5316\u4e3a\u4f4e\u7ef4\u8868\u793a\uff0c\u901a\u5e38\u662f\u4ee52\u7ef4\u7684\u5f62\u5f0f\u3002\u795e\u7ecf\u7fa4\u4f53\u6a21\u578b\u901a\u5e38\u5305\u62ec\u4f4e\u653e\u7535\u7387\u5bf9\u5e94\u7684\u4e0b\u72b6\u6001<\/span>\uff08down state\uff09<\/span>\uff0c\u9ad8\u653e\u7535\u7387\u5bf9\u5e94\u7684\u4e0a\u72b6\u6001<\/span>\uff08upstate\uff09<\/span>\uff0c\u4ee5\u53ca\u5728\u4e0a\u72b6\u6001\u4e2d\u666e\u904d\u663e\u793a\u632f\u8361\u52a8\u529b\u5b66\u7684\u80fd\u529b\u3002\u6682\u65f6\u5ffd\u7565\u632f\u8361\u52a8\u529b\u5b66\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u6982\u5ff5\u4e0a\u5c06\u5171\u5b58\u7684\u9ad8\u3001\u4f4e\u72b6\u6001\uff0c\u4ee5\u53ca\u7531\u5206\u5c94\u5bfc\u81f4\u5b83\u4eec\u7a33\u5b9a\u6027\u7684\u6539\u53d8\uff0c\u7b80\u5316\u4e3a\u5355\u4e00\u53d8\u91cfx\u7684\u76f8\u6d41\uff0c\u5982\u56fe5C\u6240\u793a\u3002\u8fd9\u91cc\u5c06\u76f8\u6d41\u7b80\u5316\u4e3a\u4e24\u79cd\u7a33\u5b9a\u72b6\u6001\u7684\u5206\u79bb\uff0c\u5916\u90e8\u63a7\u5236\u53c2\u6570\u6539\u53d8\u5bfc\u81f4\u978d\u8282\u70b9\u5206\u5c94\uff0c\u53ef\u80fd\u4f1a\u4f7f\u7cfb\u7edf\u5931\u7a33\u3002\u8be5\u6a21\u578b\u5728\u6570\u5b66\u4e0a\u4e0eWong\u2013Wang\u6a21\u578b\u4e00\u81f4\uff0c\u540e\u8005\u662f\u7531 Brunel Wang \u6a21\u578b\u5728\u9694\u7edd\u8fd1\u4f3c\u7684\u6761\u4ef6\u4e0b\u63a8\u5bfc\u5f97\u5230\u3002\u6211\u4eec\u60f3\u8981\u5f3a\u8c03\u7684\u662f\uff0c\u8fd9\u79cd\u8868\u793a\u5e76\u4e0d\u662fBrunel Wang \u795e\u7ecf\u7fa4\u4f53\u6a21\u578b\u7279\u6709\u7684\uff0c\u800c\u662f\u523b\u753b\u4e86\u6240\u6709\u795e\u7ecf\u7fa4\u4f53\u6a21\u578b\u7684\u57fa\u672c\u52a8\u529b\u5b66\u7279\u6027\uff0c\u5373\u5bf9\u4e8e\u7cfb\u5217\u4e2d\u95f4\u63a7\u5236\u53c2\u6570\uff0c\u540c\u65f6\u5b58\u5728\u4f4e\u3001\u9ad8\u653e\u7535\u72b6\u6001\uff0c\u7ecf\u63a7\u5236\u53d8\u91cf\u53d6\u9ad8\/\u4f4e\u503c\u7684\u5206\u5c94\uff0c\u4e22\u5931\u4f4e\/\u9ad8\u653e\u7535\u72b6\u6001\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u6211\u4eec\u7528\u8be5\u7b80\u5316\u795e\u7ecf\u7fa4\u4f53\u4f5c\u4e3a\u4e0b\u8282\u7b49\u53d8\u8111\u7f51\u7edc\u6a21\u578b\u7684\u57fa\u672c\u6784\u5efa\u5757\u3002<\/span><\/section>\n

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<\/section>\n

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4.2 \u7b49\u53d8\u77e9\u9635\u7684\u63a8\u5bfc<\/strong><\/span><\/section>\n

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<\/section>\n

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<\/section>\n

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\u57fa\u4e8e\u8fde\u63a5\u7ec4\u7684\u7f51\u7edc\u5efa\u6a21\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u9759\u606f\u72b6\u6001\u7684\u5927\u8111\u6d3b\u52a8[68-75]\uff0c\u4f46\u662f\u9664\u63cf\u8ff0\u6027\u7edf\u8ba1<\/span>\uff08\u5982\u529f\u80fd\u8fde\u63a5\uff0c\u529f\u80fd\u8fde\u63a5\u52a8\u529b\u5b66\uff0c\u591a\u5c3a\u5ea6\u71b5\uff09<\/span>\u548c\u5047\u8bbe\u673a\u5236<\/span>\uff08\u4e9a\u4e34\u754c\u6027\uff0c\u968f\u673a\u5171\u632f\uff09<\/span>\u5916\uff0c\u8fd8\u5e76\u672a\u6709\u4e25\u8c28\u7684\u7406\u8bba\u89c2\u70b9\u3002\u901a\u8fc7\u5f15\u5165\u8fde\u63a5\u7ec4\uff0c\u7b49\u53d8\u77e9\u9635\u7684\u5bf9\u79f0\u6027\u7834\u7f3a\u7ed9\u51fa\u4e00\u4e2a\u8ff7\u4eba\u7684\u66ff\u4ee3\u6027\u89e3\u91ca\u3002\u4f46\u662f\u5b83\u4ecd\u7136\u7f3a\u5c11\u91cd\u8981\u7684\u89e3\u91ca\u8bba\u636e\uff0c\u56e0\u4e3a\u7b49\u53d8\u77e9\u9635\u7684\u5bf9\u79f0\u6027\u7834\u7f3a\u5e76\u672a\u5e26\u6765\u5b9e\u8d28\u6027\u7684\u964d\u7ef4\u3002\u4e0d\u53d8\u6d41\u5f62\u4fdd\u6301N-1\u7ef4\u3002\u59823.3\u8282\u4e2d\u8bba\u8ff0\u90a3\u6837\uff0c\u5728\u8fd9\u91cc\u7279\u522b\u662f\u5bf9\u4e8e\u795e\u7ecf\u79d1\u5b66\u6765\u8bf4\uff0c\u95ee\u9898\u662f\uff1aN\u7ef4\u7a7a\u95f4\u4e2d\u7684\u53d8\u91cfQ(t)\u5982\u4f55\u964d\u7ef4\u5230M\u7ef4\u7a7a\u95f4\u4e2d\u7684\u53d8\u91cfq(t)\uff0c\u56e0\u4e3aM\u8fdc\u5c0f\u4e8eN\u3002<\/span><\/section>\n

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\u4e00\u4e2a\u53ef\u80fd\u7684\u5b9e\u73b0\u65b9\u6cd5\u5982\u4e0b\u3002\u5728\u66f4\u73b0\u5b9e\u7684\u795e\u7ecf\u79d1\u5b66\u6a21\u578b\u4e2d\uff0c\u4e0d\u52a8\u70b9\u4e0d\u4f1a\u76f8\u540c\u3002\u901a\u5e38\u4e0b\u72b6\u6001\u6bd4\u4e0a\u72b6\u6001\u7a33\u5b9a\u3002\u5c3d\u7ba1\u8fd9\u79cd\u5dee\u5f02\u4e0d\u53ef\u907f\u514d\u5730\u628a\u68af\u5ea6\u5f15\u5165\u5230\u7f51\u7edc\u6d41\u4e2d\uff0c\u4f46\u4ecd\u4e0d\u8db3\u4ee5\u51cf\u5c11\u4f4e\u7ef4\u6d41\u5f62\u7684\u7ef4\u5ea6\uff0c\u800c\u8fd9\u4e9b\u4f4e\u7ef4\u6d41\u5f62\u662f\u7279\u5b9a\u4efb\u52a1\u6240\u5fc5\u987b\u7684\uff0c\u4e14\u5df2\u77e5\u5728\u4eba\u7c7b\u5927\u8111\u6d3b\u52a8\u4e2d\u662f\u5b58\u5728\u7684\u3002\u6587\u732e\u91cc\u7684\u8ba8\u8bba\u662d\u793a\u53bb\u76f8\u5173\u4f5c\u4e3a\u91cd\u8981\u4fe1\u606f\u5904\u7406\u673a\u5236\u7684\u53ef\u80fd\u6027[76-78]\uff0c\u5728\u8fd9\u6216\u8bb8\u901a\u8fc7\u4e0a\u72b6\u6001\u4e2d\u7684\u632f\u8361\u80fd\u5f97\u4ee5\u5b9e\u73b0\u3002\u5728\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u4e2d\uff0c\u5229\u7528\u9891\u7387\u5206\u79bb\u6216\u5e73\u5747\u8fdb\u884c\u89e3\u8026\u662f\u5e7f\u4e3a\u4eba\u77e5\u7684\u4e00\u79cd\u673a\u5236<\/span>\uff08\u5982\u65cb\u8f6c\u6ce2\u8fd1\u4f3c\uff09<\/span>\uff0c\u5e76\u5728\u5927\u89c4\u6a21\u8111\u7f51\u7edc\u4e2d\u7528\u4e8e\u7ec4\u7ec7\u540c\u6b65[79]\u548c\u4ea4\u53c9\u9891\u7387\u8026\u5408[80]\u3002\u8fd9\u79cd\u632f\u8361\u884c\u4e3a\u7684\u80fd\u529b\u5f88\u9002\u5408\u4e8e\u5c06\u7b49\u53d8M\u7ef4\u6d41\u5f62\u53ca\u5176N-M\u7ef4\u4e92\u8865\u5b50\u7a7a\u95f4 (M<<N) \u4e4b\u95f4\u7684\u8fde\u63a5\u65ad\u5f00\uff0c\u4e3a\u5c06\u6765\u7684\u79d1\u5b66\u7814\u7a76\u63d0\u4f9b\u4e00\u6761\u6e05\u6670\u7684\u524d\u8fdb\u9053\u8def\u3002<\/span><\/section>\n

<\/strong><\/span><\/section>\n
4.3 \u6982\u7387\u5206\u5e03\u51fd\u6570\u548c\u81ea\u7531\u80fd\u7684\u63a8\u5bfc<\/strong><\/span><\/section>\n

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\u6211\u4eec\u5e0c\u671b\u901a\u8fc7\u4e24\u4e2a\u4f8b\u5b50\u6765\u9610\u8ff0\u8fd9\u4e00\u70b9\u3002\u7b2c\u4e00\u4e2a\u793a\u4f8b\u4e0e\u524d\u97624.1\u8282\u8ba8\u8bba\u7684\u60c5\u51b5\u6709\u5173\uff0c\u5176\u6709\u4e24\u4e2a\u8026\u5408\u8282\u70b9\u3002\u9996\u5148\u5c06\u7126\u70b9\u653e\u5728\u4e24\u4e2a\u7a33\u5b9a\u4e0d\u52a8\u70b9\u4e2d\u7684\u4e00\u4e2a\u4e0a\u3002\u5bf9\u5176\u6d41\u8fdb\u884c\u7ebf\u6027\u5316\uff0c\u5f97\u5230\u5982\u4e0b\u8868\u8fbe\u5f0f\uff1a<\/span><\/section>\n

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\u53e6\u4e00\u4e2a\u8bf4\u660e\u6027\u793a\u4f8b\u5982\u7b2c4.2\u8282\u4e2d\u7684\u7b49\u53d8\u77e9\u9635\u3002\u4e3a\u7b80\u5355\u8d77\u89c1\uff0c\u518d\u6b21\u5c06\u8ba8\u8bba\u9650\u5236\u5728\u4e24\u4e2a\u8282\u70b9\u4e0a\u3002\u6309\u7167\u4e0e\u524d\u4e00\u4e2a\u793a\u4f8b\u76f8\u540c\u7684\u6570\u5b66\u6b65\u9aa4\uff0c\u8026\u5408\u8282\u70b9\u7684\u52bf\u51fd\u6570\u4e3a\uff1a<\/span><\/section>\n

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\u5176\u4e2d\u03b2=1-G\u8868\u793a\u8026\u5408\u5f3a\u5ea6\uff0c\u03b2=0\u65f6\u8868\u793a\u6ca1\u6709\u8026\u5408\u3002\u540c\u524d\u9762\u4e00\u6837\uff0c\u53ef\u628a\u5e73\u7a33\u6982\u7387\u51fd\u6570\u5199\u4e3ap(x,y)=p(x|y)p(y)\uff0c\u5176\u4e2d<\/span><\/section>\n

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[68] Ghosh A, Rho Y, McIntosh A R, K\u00f6tter R and Jirsa V K 2008 Noise during rest enables the exploration of the brain\u2019s dynamic repertoire PLoS Comput. Biol. 4 e1000196<\/span><\/section>\n
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[70] Hansen E C, Battaglia D, Spiegler A, Deco G and Jirsa V K 2015 Functional connectivity dynamics: modeling the switching behavior of the resting state Neuroimage 105 525\u201335<\/span><\/section>\n
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[74] Deco G, KringelbachM L, Jirsa V K and Ritter P 2017 The dynamics of resting fluctuations in the brain: metastability and its dynamical cortical core Sci. Rep. 7 3095<\/span><\/section>\n
[75] GolosM, Jirsa V and Dauc\u00b4e E 2015 Multistability in large scale models of brain activity PLoS Comput. Biol. 11 e1004644<\/span><\/section>\n
[76] Dong DW1995 Associative decorrelation dynamics: a theory of self-organization and optimization in feedback networks Advances in Neural Information Processing Systems pp 925\u201332<\/span><\/section>\n
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