{"id":58423,"date":"2025-04-11T20:11:39","date_gmt":"2025-04-11T12:11:39","guid":{"rendered":"https:\/\/swarma.org\/?p=58423"},"modified":"2025-04-11T20:11:39","modified_gmt":"2025-04-11T12:11:39","slug":"%e7%a8%80%e7%96%8f%e6%9c%89%e5%90%91%e7%bd%91%e7%bb%9c%e4%b8%8a%e5%a4%8d%e6%9d%82%e7%b3%bb%e7%bb%9f%e7%9a%84%e5%8a%a8%e5%8a%9b%e5%ad%a6%e5%b9%b3%e5%9d%87%e5%9c%ba%e7%90%86%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=58423","title":{"rendered":"\u7a00\u758f\u6709\u5411\u7f51\u7edc\u4e0a\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba"},"content":{"rendered":"
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\u8bba\u6587\u9898\u76ee\uff1aDynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks<\/span><\/span><\/section>\n
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\u590d\u6742\u52a8\u529b\u7cfb\u7edf\u7531 N \u4e2a\u81ea\u7531\u5ea6 x<\/span>i<\/span><\/sub>(t) (i = 1,\u2026,N) \u5efa\u6a21\uff0c\u8fd9\u4e9b\u81ea\u7531\u5ea6\u6839\u636e\u5fae\u5206\u65b9\u7a0b\u968f\u65f6\u95f4\u6f14\u5316<\/span><\/span><\/p>\n


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\u5176\u4e2d {A<\/span>ij<\/span><\/sub>}<\/span>i,j = 1,<\/span>\u2026<\/span><\/span> ,N<\/span><\/sub> \u5b9a\u4e49\u4e86\u4ea4\u4e92\u7f51\u7edc\u3002\u51fd\u6570 f(x) \u63a7\u5236\u65e0\u76f8\u4e92\u4f5c\u7528\u65f6\u7684\u52a8\u529b\u5b66\uff0c\u6838\u51fd\u6570 g(x, x’) \u5219\u51b3\u5b9a\u4e86\u6210\u5bf9\u8026\u5408\u3002\u65b9\u7a0b (1) \u53ef\u7528\u4e8e\u6a21\u62df\u795e\u7ecf\u7f51\u7edc [1 – 5] \u548c\u751f\u6001\u7cfb\u7edf [6-8] \u3001\u6d41\u884c\u75c5\u4f20\u64ad [9-12]\u3001\u540c\u6b65\u73b0\u8c61 [13-15]\u3001\u89c2\u70b9\u52a8\u529b\u5b66[16-17]\u4ee5\u53ca\u591a\u5143 Onstein-Uhlenbeck \u8fc7\u7a0b [18 – 20] \u7684\u975e\u5e73\u8861\u52a8\u529b\u5b66\u3002\u8868 I \u7ed9\u51fa\u4e86\u590d\u6742\u884c\u4e3a\u5178\u578b\u6a21\u578b\u7684 <\/span>f(x)<\/span><\/span> \u548c <\/span>g(x, x’) <\/span><\/span>\u7684\u5177\u4f53\u5f62\u5f0f\u3002<\/span><\/span><\/section>\n

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\u53e6\u4e00\u65b9\u9762\uff0c\u5728\u4f0a\u8f9b\u81ea\u65cb<\/span><\/span>\uff08Ising spins\uff09<\/span><\/span>\u7cfb\u7edf\u7684\u60c5\u51b5\u4e0b\uff0c\u7a00\u758f\u7f51\u7edc\u4e0a\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u5df2\u7ecf\u5f97\u5230\u4e86\u5e7f\u6cdb\u7814\u7a76[38-50]\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7a7a\u8154\u65b9\u6cd5 [39] \u548c DMFT [38, 40] \u90fd\u80fd\u6839\u636e\u5355\u4e2a\u52a8\u529b\u5b66\u53d8\u91cf\u7684\u6709\u6548\u52a8\u529b\u5b66\u7684\u8def\u5f84\u6982\u7387\u63d0\u4f9b\u89e3\u6790\u89e3\u3002\u7136\u800c\uff0c\u53cc\u5411\u8fb9\u7684\u5b58\u5728\u4f1a\u5f15\u53d1\u65f6\u95f4\u53cd\u9988\uff0c\u5728\u7a00\u758f\u7cfb\u7edf\u7684\u7279\u5b9a\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4f1a\u5bfc\u81f4\u8def\u5f84\u6982\u7387\u7ef4\u5ea6\u5448\u6307\u6570\u589e\u957f[38,40,49]\uff0c\u4f7f\u5f97\u6570\u503c\u8ba1\u7b97\u4e0d\u53ef\u884c\u3002\u901a\u8fc7\u8fd1\u4f3c\u65b9\u6848\uff0c\u5982\u5355\u6b21\u8fd1\u4f3c [39]\uff0c\u4f7f\u8fd9\u4e9b\u8ba1\u7b97\u6210\u4e3a\u53ef\u80fd[42,43,48]\u3002\u5f53\u76f8\u4e92\u4f5c\u7528\u662f\u6709\u5411\u6216\u5355\u5411\u65f6\uff0c\u7531\u4e8e\u4e0d\u5b58\u5728\u65f6\u95f4\u53cd\u9988\uff0c\u8def\u5f84\u6982\u7387\u65b9\u7a0b\u53ef\u4ee5\u88ab\u9ad8\u6548\u5730\u6c42\u89e3[38,39,51]\u3002<\/span><\/span><\/section>\n

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\u53d7\u4f0a\u8f9b\u81ea\u65cb\u7cfb\u7edf\u7814\u7a76\u7ed3\u679c\u7684\u542f\u53d1\uff0c\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u51b3\u4e86\u7531\u65b9\u7a0b (1) \u652f\u914d\u7684\u6a21\u578b\u5728\u5177\u6709\u5f02\u8d28\u62d3\u6251\u7ed3\u6784\u7684\u7a00\u758f\u6709\u5411\u7f51\u7edc\u4e0a\u7684\u52a8\u529b\u5b66\u95ee\u9898\u3002\u8be5\u89e3\u662f\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u4e2d\u7684\u4e00\u4e2a\u57fa\u7840\u6027\u6b65\u9aa4\uff0c\u56e0\u4e3a\u5b83\u6700\u7ec8\u5c06\u590d\u6742\u7f51\u7edc\u7684\u7a00\u758f\u548c\u5f02\u8d28\u7ed3\u6784\u7eb3\u5165\u4e86 DMFT \u7684\u5f62\u5f0f\u4f53\u7cfb\u4e2d\u3002\u6709\u5411\u7f51\u7edc\u4e4b\u6240\u4ee5\u5f15\u4eba\u5173\u6ce8\uff0c\u662f\u56e0\u4e3a\u5b83\u4eec\u80fd\u591f\u5bf9\u73b0\u5b9e\u4e16\u754c\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u975e\u4e92\u6613\u76f8\u4e92\u4f5c\u7528\u8fdb\u884c\u5efa\u6a21 [52]\uff0c\u5305\u62ec\u4eba\u7c7b\u5927\u8111\u76ae\u5c42 [53]\u3001\u98df\u7269\u7f51 [37, 54, 55]\u3001\u57fa\u56e0\u8c03\u63a7\u7f51\u7edc [56, 57]\u3001\u5728\u7ebf\u793e\u4ea4\u7f51\u7edc [58, 59] \u548c\u4e07\u7ef4\u7f51 [60]\u3002\u56e0\u6b64\uff0c\u8fd9\u91cc\u63d0\u51fa\u7684\u5f62\u5f0f\u4f53\u7cfb\u4e3a\u5206\u6790\u7814\u7a76\u73b0\u5b9e\u76f8\u4e92\u4f5c\u7528\u5982\u4f55\u5f71\u54cd\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u63d0\u4f9b\u4e86\u53ef\u80fd\u6027\u3002<\/span><\/span><\/section>\n

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\u901a\u8fc7\u5c06 DMFT \u63a8\u5e7f\u5230\u7a00\u758f\u7cfb\u7edf\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u63cf\u8ff0 <\/span>N\u2192\u221e <\/span><\/span>\u4e0b\u5355\u53d8\u91cf\u6709\u6548\u52a8\u529b\u5b66\u7684\u8def\u5f84\u6982\u7387\u7684\u7cbe\u786e\u65b9\u7a0b\uff0c\u5e76\u5229\u7528\u7fa4\u4f53\u52a8\u529b\u5b66\u7b97\u6cd5 [61-66] \u6c42\u89e3\u4e86\u8868 I \u4e2d\u4e0d\u540c\u6a21\u578b\u7684\u8be5\u65b9\u7a0b\u3002\u6211\u4eec\u7684\u7406\u8bba\u7ed3\u679c\u4e0e\u6709\u9650\u7cfb\u7edf\u7684\u6570\u503c\u6a21\u62df\u4e4b\u95f4\u7684\u826f\u597d\u4e00\u81f4\u6027\u8bc1\u5b9e\u4e86\u6211\u4eec\u7684\u89e3\u9002\u7528\u4e8e\u901a\u8fc7\u4e0d\u540c\u7f51\u7edc\u62d3\u6251\u7ed3\u6784\u76f8\u4e92\u4f5c\u7528\u7684\u5404\u79cd\u975e\u7ebf\u6027\u6a21\u578b\uff0c\u5305\u62ec\u5177\u6709\u5e42\u5f8b\u5ea6\u5206\u5e03\u7684\u7f51\u7edc [36]\u3002<\/span><\/span><\/section>\n

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\u4f5c\u4e3a\u5e94\u7528\uff0c\u6211\u4eec\u786e\u5b9a\u4e86 Sompolinsky \u7b49\u4eba [1] \u63d0\u51fa\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u5728\u7a00\u758f\u72b6\u6001\u4e0b\u7684\u76f8\u56fe\u3002\u6211\u4eec\u8868\u660e\uff0c\u76f8\u56fe\u663e\u793a\u51fa\u5e73\u51e1\u548c\u975e\u5e73\u51e1\u7684\u4e0d\u52a8\u70b9\u76f8\u3001\u5e73\u5747\u6d3b\u52a8\u4e3a\u96f6\u7684\u6df7\u6c8c\u76f8\u4ee5\u53ca\u5e73\u5747\u6d3b\u52a8\u975e\u96f6\u7684\u6df7\u6c8c\u76f8 [30]\u3002\u901a\u8fc7\u8ba1\u7b97\u67d0\u4e9b\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf\uff0c\u6211\u4eec\u786e\u5b9a\u4e86\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u76f8\u53d8\u7ebf\u4f5c\u4e3a\u5e73\u5747\u5ea6\u548c\u8026\u5408\u5f3a\u5ea6\u65b9\u5dee\u7684\u51fd\u6570\uff0c\u8868\u660e\u5b83\u4eec\u4e0e\u4ece\u968f\u673a\u77e9\u9635\u7406\u8bba\u63a8\u5bfc\u51fa\u6765\u7684\u666e\u9002\u4e34\u754c\u7ebf\u4e00\u81f4 [67 – 69]\u3002\u7279\u522b\u5730\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u6570\u503c\u8bc1\u636e\uff0c\u8868\u660e\u6df7\u6c8c\u76f8\u4e4b\u95f4\u7684\u8f6c\u53d8\u4e0e\u76f8\u4e92\u4f5c\u7528\u77e9\u9635\u7684\u4e3b\u7279\u5f81\u503c\u548c\u6b21\u4e3b\u7279\u5f81\u503c\u4e4b\u95f4\u7684\u95f4\u9699\u6d88\u5931\u76f8\u543b\u5408\u3002<\/span><\/span><\/section>\n


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\u8bbe A<\/span>ij<\/span><\/sub>= C<\/span>ij<\/span><\/sub>J<\/span>ij <\/span><\/sub>\u4e3a N\u00d7N \u76f8\u4e92\u4f5c\u7528\u77e9\u9635 <\/span>A<\/span><\/strong> \u7684\u5143\u7d20\u3002\u4e8c\u5143\u53d8\u91cf C<\/span>ij<\/span><\/sub>\u2208<\/span><\/span>{0,1<\/span>} <\/span><\/span>\u786e\u5b9a\u7f51\u7edc\u62d3\u6251\u7ed3\u6784\uff0c\u800c <\/span>\"image.png\" <\/span><\/sub>\u63a7\u5236\u76f8\u4e92\u4f5c\u7528\u5f3a\u5ea6\u3002\u5982\u679c <\/span>C<\/span><\/span>ij<\/span><\/sub> = 1\uff0c\u5219\u5b58\u5728\u4e00\u6761\u4ece\u8282\u70b9 j \u6307\u5411 i \u7684\u6709\u5411\u8fb9 j\u2192i\uff0c\u5426\u5219 <\/span> C<\/span><\/span>ij<\/span><\/sub> =<\/span><\/span> 0\u3002\u5165\u5ea6 <\/span><\/span>\"image.png\" <\/span><\/sub>\u548c\u51fa\u5ea6 <\/span>\"image.png\"<\/span><\/sub> \u5206\u522b\u8ba1\u7b97\u8fdb\u5165\u548c\u79bb\u5f00\u8282\u70b9 i \u7684\u94fe\u63a5\u6570\u91cf [36]\u3002\u968f\u673a\u53d8\u91cf {C<\/span><\/span>ij<\/span><\/sub>}<\/span><\/span>i\u2260j<\/span><\/sub> \u9075\u5faa\u5206\u5e03<\/span><\/span><\/section>\n

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\u5176\u4e2d<\/span>\"image.png\"<\/span><\/sub>\u662f\u5f52\u4e00\u5316\u5e38\u6570\u4e14 C<\/span>ii<\/span><\/sub> = 0\u3002\u5ea6 {K<\/span>i<\/span><\/sub>, L<\/span>i<\/span><\/sub>}<\/span>i = 1,\u2026,N<\/span><\/sub> \u662f\u4ece <\/span>\"image.png\"<\/span><\/sub> \u4e2d\u62bd\u53d6\u7684\u72ec\u7acb\u540c\u5206\u5e03\u968f\u673a\u53d8\u91cf\uff0c\u5176\u4e2d p<\/span>in,k<\/span><\/sub> \u548c<\/span> <\/span><\/span>\"image.png\"<\/span><\/sub> <\/span><\/span>\u5206\u522b\u662f\u5165\u5ea6\u548c\u51fa\u5ea6\u5206\u5e03 [36,64]\u3002\u53c2\u6570 c \u662f\u5e73\u5747\u5ea6<\/span><\/span><\/section>\n

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\u65b9\u7a0b (2) \u5b9a\u4e49\u4e86\u4e00\u4e2a\u7f51\u7edc\u96c6\u5408\uff0c\u5176\u4e2d\u6709\u5411\u94fe\u63a5\u4ee5\u6982\u7387 c\/N \u968f\u673a\u653e\u7f6e\u5728\u8282\u70b9\u5bf9\u4e4b\u95f4\uff0c\u670d\u4ece <\/span>\"image.png\"<\/span><\/sub> \u751f\u6210\u7684\u9884\u8bbe\u5ea6\u5e8f\u5217\u3002\u5728 <\/span>N\u2192\u221e<\/span><\/span> \u7684\u6781\u9650\u60c5\u51b5\u4e0b\uff0c\u4ece\u65b9\u7a0b (2) \u751f\u6210\u7684\u7f51\u7edc\u6837\u672c\u4e0e\u7531\u914d\u7f6e\u6a21\u578b[70,71]\u751f\u6210\u7684\u6837\u672c\u76f8\u4f3c\u3002\u8026\u5408\u5f3a\u5ea6 {J<\/span>ij<\/span><\/sub>}<\/span>i,j = 1,<\/span>\u2026<\/span><\/span> ,N<\/span><\/sub> \u662f\u4ece\u5747\u503c\u4e3a <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> \u3001\u65b9\u5dee\u4e3a <\/span>\"image.png\"<\/span><\/sub> \u7684\u5206\u5e03 <\/span>p<\/span><\/span>J<\/span><\/sub> <\/span><\/span> \u4e2d\u62bd\u53d6\u7684\u72ec\u7acb\u540c\u5206\u5e03\u968f\u673a\u53d8\u91cf\u3002\u5206\u5e03 <\/span>\"image.png\"<\/span><\/sub> \u548c p<\/span>J<\/span><\/sub> \u5b8c\u5168\u786e\u5b9a\u4e86\u7f51\u7edc\u96c6\u5408\uff0c\u4ece\u800c\u53ef\u4ee5\u7cfb\u7edf\u5730\u7814\u7a76\u7f51\u7edc\u5f02\u8d28\u6027\u5982\u4f55\u5f71\u54cd\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u3002<\/span><\/span><\/section>\n

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\u901a\u8fc7\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u6c42\u89e3<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u6211\u4eec\u4f7f\u7528\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba<\/span><\/span> (DMFT) <\/span><\/span>[24 – 26] \u6c42\u89e3\u65b9\u7a0b (1) \u5728\u6709\u5411\u7f51\u7edc\u4e0a\u7684\u8026\u5408\u52a8\u529b\u5b66\u3002\u6211\u4eec\u8003\u8651\u7a00\u758f\u72b6\u6001\uff0c\u5176\u4e2d\u5e73\u5747\u5ea6 c \u662f\u6709\u9650\u7684\uff0c\u4e0e N \u65e0\u5173\u3002\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u57fa\u4e8e\u751f\u6210\u6cdb\u51fd<\/span><\/span><\/section>\n

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\u5728\u56fa\u5b9a\u65f6\u95f4\u533a\u95f4\u5185\u89c2\u5bdf\u5230\u72b6\u6001\u53d8\u91cf\u7684\u52a8\u529b\u5b66\u8def\u5f84 <\/span>x<\/span><\/strong>(t)  = (x<\/span>1<\/span><\/sub>(t) ,\u2026,x<\/span>N<\/span><\/sub>(t) \u7684\u6982\u7387\u5bc6<\/span>\u5ea6<\/span><\/span> <\/span>\"image.png\"<\/span><\/sub>\u3002<\/span>{<\/span><\/span>x<\/span>i<\/span><\/sub>(t)}<\/span>i = 1,<\/span>\u2026<\/span><\/span> ,N<\/span><\/sub>\u7684\u76f8\u5173\u51fd\u6570\u53ef\u7531<\/span>\"image.png\"<\/span><\/sub> \u5173\u4e8e\u5916\u90e8\u6e90 <\/span>\"image.png\"<\/span><\/sub> \u7684\u5bfc\u6570\u5f97\u51fa\u3002\u5c40\u90e8\u53d8\u91cf x<\/span>i<\/span><\/sub>(t) \u7684 n \u9636\u77e9<\/span><\/span><\/section>\n

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\u663e\u7136\uff0c<\/span>\"image.png\"<\/span><\/sub> \u6ee1\u8db3 <\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/section>\n

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\u5728\u6587\u732e [72] \u4e2d\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u5bf9\u4e8e\u6709\u9650\u7684 c<\/span>\uff0c<\/span><\/span>\"image.png\"<\/span><\/sub> <\/span><\/span>\u5728\u7531\u5f0f (2) \u5b9a\u4e49\u7684\u7f51\u7edc\u96c6\u5408\u4e0a\u7684\u5e73\u5747\u503c\uff0c\u5c06\u95ee\u9898\u8f6c\u5316\u4e3a\u978d\u70b9\u79ef\u5206\u7684\u6c42\u89e3\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u6211\u4eec\u5bf9\u5e8f\u53c2\u91cf\u7ed9\u51fa\u4e86\u6e05\u6670\u7684\u7269\u7406\u89e3\u91ca\uff0c\u7b80\u5316\u4e86\u978d\u70b9\u65b9\u7a0b\uff0c\u5e76\u5f97\u5230\u4e86\u7a00\u758f\u533a\u57df\u52a8\u529b\u5b66\u7684\u53ef\u884c\u89e3\u3002\u5728 <\/span>N\u2192\u221e<\/span><\/span> \u7684\u6781\u9650\u60c5\u51b5\u4e0b\uff0c\u5fae\u89c2\u52a8\u529b\u5b66\u53d8\u91cf\u89e3\u8026\uff0c\u5355\u4e2a\u53d8\u91cf x(t) \u7684\u6709\u6548\u52a8\u529b\u5b66\u7684\u8def\u5f84\u6982\u7387 <\/span>\"image.png\"<\/span><\/sub> \u7531\u4e0b\u5f0f\u786e\u5b9a<\/span><\/span><\/section>\n

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\u5176\u4e2d <\/span>\u03b4<\/span><\/span>F<\/span><\/sub> \u662f\u72c4\u62c9\u514b -\u03b4 \u6cdb\u51fd\u3002\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf\u7531 m(t)  =<\/span>\u3008<\/span>x(t)<\/span><\/span>\u3009<\/span><\/span>*<\/span><\/sub> \u548c q<\/span>(t)  =<\/span><\/span>\u3008<\/span>x<\/span>2<\/span><\/sup>(t)<\/span><\/span>\u3009<\/span><\/span>*<\/span><\/sub> \u8ba1\u7b97\u5f97\u51fa\uff0c\u5176\u4e2d<\/span><\/span><\/section>\n

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\u662f\u7531<\/span> <\/span><\/span>\"image.png\"<\/span><\/sub> \u652f\u914d\u4e0b\u6709\u6548\u52a8\u529b\u5b66\u7684\u5e73\u5747\u91cf\u3002\u81ea\u6d3d\u65b9\u7a0b (7) \u662f\u5177\u6709\u5c40\u90e8\u6811\u72b6\u7ed3\u6784\u7684\u7a00\u758f\u6709\u5411\u7f51\u7edc [73] \u4e0a\u4e00\u5927\u7c7b\u6a21\u578b\uff08\u89c1\u8868 I\uff09\u7684\u7cbe\u786e\u89e3\uff0c\u5176\u4e2d\u5165\u5ea6\u548c\u51fa\u5ea6\u5177\u6709\u4efb\u610f\u5206\u5e03 p<\/span>J<\/span><\/sub> \u548c<\/span> <\/span><\/span>\"image.png\"<\/span><\/sub> <\/span><\/span>\u3002\u5728\u6587\u732e [72] \u4e2d\uff0c\u6211\u4eec\u5904\u7406\u4e86\u5728\u5165\u5ea6\u548c\u51fa\u5ea6\u76f8\u5173\u7684\u7f51\u7edc\u4e0a\u5177\u6709\u9ad8\u65af\u52a0\u6027\u566a\u58f0\u7684\u52a8\u529b\u5b66\u6a21\u578b\u7684\u66f4\u4e00\u822c\u60c5\u51b5\u3002\u65b9\u7a0b (7) \u7684\u89e3\u786e\u5b9a\u4e86\u5728 <\/span>N\u2192\u221e<\/span><\/span> \u6781\u9650\u4e0b\u5fae\u89c2\u53d8\u91cf\u7684\u5168\u6982\u7387\u5206\u5e03\u7684\u65f6\u95f4\u6f14\u5316\u3002<\/span><\/span><\/section>\n

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\u56fe 1. SIS \u6a21\u578b\u3001LV \u6a21\u578b\u548c NN \u6a21\u578b\u7684\u5747\u503c m(t) \u548c\u6807\u51c6\u5dee <\/span>\"image.png\"<\/span><\/sub><\/span> \u7684\u52a8\u6001\u53d8\u5316\uff08\u89c1\u8868 I\uff09\u3002\u7ed3\u679c\u5c55\u793a\u4e86\u5e73\u5747\u5ea6\u4e3a c = 5 \u7684\u6709\u5411\u968f\u673a\u7f51\u7edc\u4ee5\u53ca\u4e24\u79cd\u5165\u5ea6\u5206\u5e03\uff08\u5f0f (9)\uff09\u7684\u60c5\u51b5\uff1a\u6cca\u677e\u5206\u5e03\uff08\u5de6\u5217\uff09\u548c\u51e0\u4f55\u5206\u5e03\uff08\u53f3\u5217\uff09\u3002\u8026\u5408\u5f3a\u5ea6\u7684\u5206\u5e03 p<\/span>J<\/span><\/sub> \u7684\u5747\u503c\u4e3a <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> \uff0c\u6807\u51c6\u5dee\u4e3a<\/span><\/span>\u03c3<\/span><\/span>J <\/span><\/span><\/sub>= 0.1\u3002\u5bf9\u4e8e LV \u6a21\u578b\u548c NN \u6a21\u578b\uff0c<\/span>p<\/span><\/span>J<\/span><\/sub> \u662f\u9ad8\u65af\u5206\u5e03\uff1b\u5bf9\u4e8e SIS \u6a21\u578b\uff0c<\/span>p<\/span><\/span>J<\/span><\/sub> \u662f\u5747\u5300\u5206\u5e03\u3002\u5b9e\u7ebf\u662f\u4f7f\u7528\u5177\u6709 5\u00d710<\/span>4<\/span><\/sup> \u6761\u8def\u5f84\u548c\u521d\u59cb\u6761\u4ef6 x<\/span>i<\/span><\/sub>(0)  = 10<\/span>-3<\/span><\/sup>\u3002\u56fe\u4e2d\u7684\u7b26\u53f7\u8868\u793a\u5bf9\u7531\u5177\u6709 4000 \u4e2a\u8282\u70b9\u7684\u6a21\u578b\u751f\u6210\u7684 10 \u4e2a\u968f\u673a\u7f51\u7edc\u8fdb\u884c\u6570\u503c\u6a21\u62df\u7684\u7ed3\u679c\u3002\u8fd9\u4e9b\u7f51\u7edc\u6784\u6210\u4e86\u4e00\u4e2a\u96c6\u5408\uff0c\u6a21\u62df\u8fc7\u7a0b\u57fa\u4e8e\u516c\u5f0f\uff081\uff09\u5c55\u5f00\u3002\u5782\u76f4\u6761\u8868\u793a\u5b8f\u89c2\u53ef\u89c2\u6d4b\u91cf\u7684\u6807\u51c6\u5dee\u3002<\/span><\/span><\/span><\/p>\n


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\u65b9\u7a0b (7) \u5728\u5f62\u5f0f\u4e0a\u4e0e\u7a00\u758f\u65e0\u5e8f\u7cfb\u7edf\u7814\u7a76\u4e2d\u51fa\u73b0\u7684\u5176\u4ed6\u5206\u5e03\u65b9\u7a0b\u76f8\u4f3c [61-66]\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7fa4\u4f53\u52a8\u529b\u5b66\u7b97\u6cd5[61,63,64] \u5bf9\u8be5\u65b9\u7a0b\u8fdb\u884c\u6570\u503c\u6c42\u89e3\u3002\u5728\u8be5\u7b97\u6cd5\u7684\u6807\u51c6\u7248\u672c[61,64]\u4e2d\uff0c\u6982\u7387\u5bc6\u5ea6\u7531\u4e00\u7ec4\u968f\u673a\u53d8\u91cf\u53c2\u6570\u5316\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u901a\u8fc7\u5f15\u5165\u4e00\u7ec4\u52a8\u6001\u8f68\u8ff9\u6765\u63a8\u5e7f\u8be5\u7b97\u6cd5\u4ee5\u8ba1\u7b97<\/span> <\/span><\/span>\"image.png\"<\/span><\/sub>\u3002\u5728\u6bcf\u6b21\u8fed\u4ee3\u6b65\u9aa4\u4e2d\uff0c\u4ece\u79cd\u7fa4\u4e2d\u968f\u673a\u9009\u62e9\u4e00\u6761\u8def\u5f84\uff0c\u5e76\u6839\u636e\u5f0f (7) \u4e2d\u7684\u5305\u542b\u72c4\u62c9\u514b –<\/span>\u03b4<\/span><\/span>F<\/span><\/sub> \u7684\u5fae\u5206\u65b9\u7a0b\u8fdb\u884c\u66f4\u65b0\u3002\u7ecf\u8fc7\u8db3\u591f\u7684\u8fed\u4ee3\u540e\uff0c\u8def\u5f84\u79cd\u7fa4\u6536\u655b\u5230\u4e00\u4e2a\u7a33\u6001\u5206\u5e03\uff0c\u4ece\u800c\u4e3a<\/span> <\/span><\/span>\"image.png\" <\/span><\/sub>\u63d0\u4f9b\u6570\u503c\u89e3\u3002\u8be5\u7b97\u6cd5\u7684\u8be6\u7ec6\u8bf4\u660e\u89c1\u6587\u732e [72]\u3002<\/span><\/span><\/section>\n

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\u5728\u56fe 1 \u4e2d\uff0c\u6211\u4eec\u5c06\u5f0f (7) \u7684\u89e3\u4e0e\u6709\u9650 N \u60c5\u51b5\u4e0b\u539f\u59cb\u8026\u5408\u52a8\u529b\u5b66\u65b9\u7a0b (1) \u7684\u6570\u503c\u6a21\u62df\u7ed3\u679c\u8fdb\u884c\u4e86\u6bd4\u8f83\u3002\u8fd9\u4e9b\u56fe\u5c55\u793a\u4e86\u4e0d\u540c\u7f51\u7edc\u62d3\u6251\u7ed3\u6784\u548c\u8868 I \u4e2d\u7684\u4e09\u79cd\u6a21\u578b<\/span><\/span>\uff08\u6587\u732e [1] \u4e2d\u7684 NN \u6a21\u578b\u3001LV \u6a21\u578b\u548c\u6d41\u884c\u75c5\u4f20\u64ad\u7684 SIS \u6a21\u578b\uff09<\/span><\/span>\u4e0b\u5fae\u89c2\u53d8\u91cf\u7684\u5747\u503c m(t) \u548c\u6807\u51c6\u5dee <\/span>\"image.png\" <\/span><\/sub>\u7684\u65f6\u95f4\u6f14\u5316\u3002\u56fe 1 \u4e2d\u7684\u7ed3\u679c\u662f\u9488\u5bf9\u6cca\u677e\u5165\u5ea6\u548c\u51e0\u4f55\u5165\u5ea6\u7684\u60c5\u51b5\uff0c\u5176\u4e2d p<\/span>in,k<\/span><\/sub> \u7531\u4e0b\u5f0f\u7ed9\u51fa<\/span><\/span><\/section>\n

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\u5728\u6587\u732e [72] \u4e2d\uff0c\u6211\u4eec\u8fd8\u5bf9\u53e6\u5916\u4e24\u79cd\u60c5\u51b5\u5c06\u5f0f (7) \u7684\u89e3\u4e0e\u6570\u503c\u6a21\u62df\u7ed3\u679c\u8fdb\u884c\u4e86\u6bd4\u8f83\uff1a\u5e42\u5f8b\u5165\u5ea6\u5206\u5e03\u7f51\u7edc\u4e0a\u7684 NN \u6a21\u578b\u4ee5\u53ca\u6d41\u884c\u75c5\u9608\u503c\u4e0b\u7684 SIS \u6a21\u578b\u3002\u5728\u6240\u6709\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u5173\u4e8e <\/span>N\u2192\u221e<\/span><\/span> \u7684\u7406\u8bba\u7ed3\u679c\u4e0e\u5927 N \u60c5\u51b5\u4e0b\u7684\u6570\u503c\u6a21\u62df\u7ed3\u679c\u90fd\u975e\u5e38\u543b\u5408\uff0c\u8bc1\u5b9e\u4e86\u5f0f (7) \u7684\u7cbe\u786e\u6027\u3002<\/span><\/span><\/section>\n

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\u4e00\u4e2a\u91cd\u8981\u7684\u95ee\u9898\u662f\uff0c\u5f53 c<\/span>\u2192\u221e<\/span><\/span>  [1,4,28,30]\u65f6\uff0c\u65b9\u7a0b (7) \u662f\u5426\u80fd\u6062\u590d\u5168\u8fde\u63a5\u6a21\u578b\u7684\u89e3\u6790\u7ed3\u679c\u3002\u5728\u70ed\u529b\u5b66\u6781\u9650 <\/span>N\u2192\u221e<\/span><\/span> \u4e4b\u540e\u53d6\u6781\u9650 <\/span>c<\/span><\/span>\u2192\u221e<\/span><\/span>\uff0c\u5b9e\u9645\u4e0a\u662f\u5728\u8003\u8651\u6807\u5ea6\u673a\u5236\uff0c\u5176\u4e2d c\u221dN<\/span>a<\/span><\/sup>\uff0c\u4e14 0 < a < 1 [74 – 77]\u3002\u6211\u4eec\u5728\u6587\u732e [72] \u4e2d\u8868\u660e\uff0c\u5728\u6781\u9650 <\/span>c<\/span><\/span>\u2192\u221e<\/span><\/span> \u4e0b\uff0c\u5ea6\u7684\u6da8\u843d\u4ecd\u7136\u663e\u8457\uff0c\u5e76\u4e14<\/span> <\/span><\/span>\"image.png\"<\/span><\/sub> \u53d6\u51b3\u4e8e\u91cd\u6574\u5316\u5165\u5ea6 \u03ba<\/span>i <\/span><\/sub>= K<\/span>i<\/span><\/sub>\/c(i = 1,\u2026 ,N) \u7684\u5b8c\u6574\u5206\u5e03<\/span><\/span>\u03bd<\/span>in<\/span><\/sub>(<\/span><\/span>\u03ba)<\/span><\/span> =\u03b4(\u03ba- 1)\u3002\u53ea\u6709\u5f53 <\/span>\u03bd<\/span>in<\/span><\/sub>(<\/span><\/span>\u03ba)<\/span><\/span> =\u03b4(\u03ba- 1) <\/span><\/span>\u65f6\uff0c\u624d\u80fd\u6062\u590d\u5168\u8fde\u63a5\u7f51\u7edc\u4e0a\u8457\u540d\u6709\u6548\u52a8\u529b\u5b66\u3002\u7531\u4e8e\u5ea6\u7684\u6da8\u843d\u5bfc\u81f4\u5168\u8fde\u63a5\u6a21\u578b\u666e\u9002\u6027\u7684\u7834\u574f\u5728\u6587\u732e [74 – 77] \u4e2d\u5df2\u88ab\u9884\u89c1\u3002<\/span><\/span><\/section>\n

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\u795e\u7ecf\u7f51\u7edc\u7684\u76f8\u56fe<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u4e3a\u4e86\u5c55\u793a\u65b9\u7a0b (7) \u7684\u4f18\u52bf\u53ca\u5176\u5177\u4f53\u5e94\u7528\uff0c\u6211\u4eec\u63a8\u5bfc\u4e86\u7a00\u758f\u6709\u5411\u7f51\u7edc\u4e0a\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u76f8\u56fe\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<\/span>\"image.png\" <\/span><\/sub>\u8868\u793a\u795e\u7ecf\u5143 i,f(x)  = x \u5904\u7684\u7a81\u89e6\u7535\u6d41\uff0c\u4e14 g( {x, x’)  = tanh(<\/span>x’) <\/span><\/span>\u3002\u8ba9\u6211\u4eec\u6839\u636e <\/span>A<\/span><\/strong> \u7684\u590d\u7279\u5f81\u503c <\/span>\"image.png\" <\/span><\/sub>\u7684\u5b9e\u90e8\u5c06\u5b83\u4eec\u6392\u5e8f\u4e3a <\/span>\"image.png\"<\/span><\/sub>\u3002\u5bf9\u65b9\u7a0b (1) \u7684\u7ebf\u6027\u7a33\u5b9a\u6027\u5206\u6790\u8868\u660e\uff0c\u5982\u679c <\/span>\"image.png\"<\/span><\/sub> < 1 \uff0c\u5219 x = 0 \u662f\u7a33\u5b9a\u7684\u3002\u57fa\u4e8e\u6587\u732e [67-69] \u4e2d\u5173\u4e8e\u6709\u5411\u7f51\u7edc\u8c31\u7684\u89e3\u6790\u7ed3\u679c\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u53ea\u8981 c < c<\/span>stab<\/span><\/sub> \uff0c\u5e73\u51e1\u4e0d\u52a8\u70b9\u5c31\u662f\u7a33\u5b9a\u7684\uff0c\u5176\u4e2d<\/span><\/span><\/section>\n

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\u65b9\u7a0b (10) \u4e2d\u7684\u4e24\u79cd\u4e0d\u540c\u72b6\u6001\u6e90\u4e8e <\/span>A <\/span><\/strong>\u7684\u8c31\u4e2d\u7684\u80fd\u9699-\u65e0\u80fd\u9699\u8f6c\u53d8 [67]\u3002\u5bf9\u4e8e <\/span>\"image.png\"<\/span><\/sub>\uff0c\u5f53 <\/span>N\u2192\u221e<\/span><\/span> \u65f6\uff0c\u8c31\u9699 |<\/span>\u03bb<\/span><\/span>1<\/span><\/span><\/sub><\/span>–<\/span>\u03bb<\/span><\/span>2<\/span><\/sub><\/span><\/span>| \u4fdd\u6301\u6709\u9650\uff0c\u800c\u5f53 <\/span>\"image.png\"<\/span><\/sub> \u65f6\uff0c\u8c31\u9699\u6d88\u5931\u3002\u65b9\u7a0b (10) \u9002\u7528\u4e8e \u03bc<\/span>J<\/span><\/sub> > 0 \u548c c > 1\u3002\u6761\u4ef6 c > 1 \u786e\u4fdd\u5177\u6709\u5ea6\u5206\u5e03 <\/span>\"image.png\" <\/span><\/sub>\u7684\u6709\u5411\u7f51\u7edc\u5305\u542b\u4e00\u4e2a\u5de8\u5927\u7684\u5f3a\u8fde\u901a\u5206\u91cf [78, 79]\uff0c\u8fd9\u610f\u5473\u7740 <\/span>A<\/span><\/strong> \u7684\u7279\u5f81\u503c\u5206\u5e03\u4e2d\u5b58\u5728\u4e00\u4e2a\u8fde\u7eed\u90e8\u5206 [68]\u3002<\/span><\/span><\/section>\n

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\u56fe 2. \u5bf9\u4e8e <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> = 0, <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> \uff1e 1 \u548c 0 < <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> < 1 \u7684\u795e\u7ecf\u7f51\u7edc\uff08NN\uff09\u6a21\u578b\u7684\u76f8\u56fe (c, \u03c3<\/span>J<\/span><\/sub>)\u3002\u5e73\u5747\u7a81\u89e6\u7535\u6d41 m(t) \u5206\u522b\u5728\u76f8 I \u548c\u76f8 II \u4e2d\u5f1b\u8c6b\u5230\u5e73\u51e1\u548c\u975e\u5e73\u51e1\u7684\u4e0d\u52a8\u70b9\u3002\u5728\u6df7\u6c8c\u76f8 III \u548c\u76f8 IV \u4e2d\uff0c<\/span>m(t)<\/span><\/span> \u5206\u522b\u56f4\u7ed5\u96f6\u503c\u548c\u975e\u96f6\u503c\u5448\u73b0\u975e\u5468\u671f\u6027\u632f\u8361\uff08\u89c1\u56fe 4\uff09\u3002\u5728 c = 1 \u5904\u7684\u70b9\u5212\u7ebf\u6807\u8bb0\u4e86\u6e17\u6d41\u9608\u503c\uff0c\u800c\u865a\u7ebf\u66f2\u7ebf\u6807\u8bc6\u4e86\u80fd\u9699 – \u65e0\u9699\u8f6c\u53d8\u3002\u5706\u5708\u548c\u83f1\u5f62\u8868\u793a\u754c\u5b9a\u76f8 IV \u7684\u8f6c\u53d8\u7ebf\u7684\u6570\u503c\u7ed3\u679c\uff08\u89c1\u6b63\u6587\uff09\uff0c\u8fd9\u4e9b\u7ed3\u679c\u662f\u901a\u8fc7\u6c42\u89e3\u65b9\u7a0b (7) \u5f97\u5230\u7684\uff0c\u91c7\u7528\u7fa4\u4f53\u52a8\u529b\u5b66\u6a21\u62df\uff0c\u8003\u8651 5 \u00d710<\/span>4<\/span><\/sup> \u6761\u8def\u5f84\uff0c\u5e76\u5047\u8bbe\u8f93\u5165\u4fe1\u53f7\u9075\u5faa\u6cca\u677e\u5206\u5e03\uff0c\u9009\u5b9a <\/span>\u03bc<\/span><\/span>J<\/span><\/sub>(<\/span>\u03bc<\/span><\/span>J<\/span><\/sub>= 1\/3 \u548c <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> = 3\/2) \u4e24\u4e2a\u53c2\u6570\u503c\u3002\u7ea2\u70b9\u6807\u8bb0 <\/span>\"image.png\"<\/span><\/sub>\u3002<\/span><\/span><\/p>\n


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\u6211\u4eec\u5f3a\u8c03\uff0c\u5e73\u51e1\u89e3\u7684\u7ebf\u6027\u7a33\u5b9a\u6027\u5206\u6790\u65e0\u6cd5\u63d0\u4f9b\u5173\u4e8e\u5f53 <\/span>x<\/span><\/strong> = 0 \u53d8\u5f97\u4e0d\u7a33\u5b9a\u65f6\u51fa\u73b0\u7684\u5f1b\u8c6b\u52a8\u529b\u5b66\u6216\u7a33\u6001\u89e3\u7684\u4fe1\u606f<\/span><\/span>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u901a\u8fc7\u6c42\u89e3\u65b9\u7a0b (7) \u6765\u7814\u7a76 NN \u6a21\u578b\u7684\u52a8\u529b\u5b66\u548c\u7a33\u6001\u3002\u56fe 2 \u5c55\u793a\u4e86\u9488\u5bf9\u4e0d\u540c <\/span><\/span>\u03bc<\/span><\/span>J<\/span><\/sub> \u533a\u57df\u5f97<\/span><\/span>\u5230\u7684\u76f8\u56fe\u3002\u5728\u76f8 I \u4e2d\uff0c<\/span>m(t)<\/span><\/span> \u4ee5\u6307\u6570\u7ea7\u5feb\u901f\u5f1b\u8c6b\u5230\u5e73\u51e1\u89e3 m = 0\uff0c\u800c\u5728\u76f8 II \u4e2d\uff0c<\/span>m(t)<\/span><\/span> \u6f14\u5316\u5230\u4e00\u4e2a\u975e\u96f6\u4e0d\u52a8\u70b9\u3002\u5728\u76f8 III \u548c\u76f8 IV \u4e2d\uff0c\u795e\u7ecf\u7f51\u7edc\u5448\u73b0\u51fa\u6df7\u6c8c\u6d3b\u52a8\uff0c\u5176\u7279\u5f81\u662f <\/span>m(t)<\/span><\/span> [1,30] \u7684\u7f13\u6162\u4e14\u975e\u5468\u671f\u6027\u632f\u8361\u3002\u754c\u5b9a\u76f8 I \u7684\u7a33\u5b9a\u7ebf\u662f\u666e\u9002\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u4ec5\u53d6\u51b3\u4e8e p<\/span>J<\/span><\/sub> \u548c p<\/span>in,k<\/span><\/sub> \u7684\u4e00\u9636\u548c\u4e8c\u9636\u77e9\u3002<\/span><\/span><\/section>\n

<\/span><\/span><\/section>\n
\u56fe 3 \u63cf\u8ff0\u4e86\u4e0d\u52a8\u70b9\u76f8 I \u548c\u76f8 II \u4e4b\u95f4\u7684\u8f6c\u53d8\u3002\u5f53 c \u4ece\u4e0a\u65b9\u63a5\u8fd1\u4e34\u754c\u5e73\u5747\u5ea6<\/span><\/span>\"image.png\" <\/span><\/sub>\u65f6\uff0c\u975e\u5e73\u51e1\u4e0d\u52a8\u70b9 m=<\/span>m(t)<\/span><\/span> \u8fde\u7eed\u6d88\u5931\u3002\u4e34\u754c\u70b9 c<\/span>*<\/span><\/sup> \u4e0e <\/span>p<\/span><\/span>in,k<\/span><\/sub> \u65e0\u5173\uff0c\u5e76\u4e14 <\/span>m(t)<\/span><\/span> \u5728\u76f8 I \u548c\u76f8 II \u5185\u4ee5\u6307\u6570\u7ea7\u5feb\u901f\u5f1b\u8c6b\u3002\u7531\u4e8e\u4e34\u754c\u6162\u5316\uff0c\u65b9\u7a0b (7) \u7684\u6570\u503c\u89e3\u5728 <\/span>c<\/span><\/span>*<\/span><\/sup> \u9644\u8fd1\u7684\u8ba1\u7b97\u8981\u6c42\u66f4\u9ad8\u3002\u5728\u76f8 II \u4e2d\uff0c\u795e\u7ecf\u5143\u653e\u7535\u7387\u6f14\u5316\u5230\u5177\u6709\u6709\u9650\u65b9\u5dee\u7684\u7a33\u6001\u5206\u5e03\u3002<\/span><\/span><\/section>\n

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\u56fe 3. \u6709\u5411\u968f\u673a\u7f51\u7edc\u4e0a NN \u6a21\u578b\u7684\u4e0d\u52a8\u70b9\u76f8\u4e4b\u95f4\u7684\u8fde\u7eed\u76f8\u53d8\u3002\u8026\u5408\u5f3a\u5ea6\u9075\u5faa\u5747\u503c\u4e3a <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> = 1\/3\u3001\u6807\u51c6\u5dee\u4e3a<\/span> <\/span><\/span><\/span>\u03c3<\/span><\/span>J<\/span><\/sub> = 0.1 \u7684\u9ad8\u65af\u5206\u5e03\u3002\u7ed3\u679c\u4f7f\u7528\u5177\u6709 5\u00d710<\/span>4<\/span><\/sup> \u6761\u8def\u5f84\u7684\u7fa4\u4f53\u52a8\u529b\u5b66\u4ece\u65b9\u7a0b (7) \u63a8\u5bfc\u5f97\u51fa\u3002(a) \u5bf9\u4e8e\u6cca\u677e\u548c\u51e0\u4f55\u5165\u5ea6\uff08\u65b9\u7a0b (9)\uff09\uff0c\u5b9a\u70b9\u89e3 m(t)  = m \u4f5c\u4e3a c \u7684\u51fd\u6570\u3002(b) \u5bf9\u4e8e\u6cca\u677e\u5165\u5ea6\u548c\u521d\u59cb\u6761\u4ef6 x<\/span>i<\/span><\/sub>(0)  = 1\uff0c<\/span><\/span> m(t)<\/span><\/span>\u5728\u8f6c\u53d8\u8fc7\u7a0b\u4e2d\u7684\u5f1b\u8c6b\u52a8\u529b\u5b66\u3002\u5bf9\u4e8e<\/span>\"image.png\"<\/span><\/sub>\uff0c\u5f53 t<\/span><\/span>\u2192\u221e<\/span><\/span> \u65f6<\/span><\/span>\uff0c<\/span> m(t)<\/span><\/span> \u5176\u4ee5\u6307\u6570\u5f62\u5f0f\u5f1b\u8c6b\u5230 m = 0\u3002<\/span><\/span><\/p>\n


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\u56fe 4 \u5c55\u793a\u4e86\u5728\u51e0\u79cd\u521d\u59cb\u6761\u4ef6\u4e0b\uff0cm(t) \u5728\u6df7\u6c8c\u76f8\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u3002\u7ecf\u8fc7\u4e00\u6bb5\u8fc7\u6e21\u65f6\u95f4 T<\/span>tr<\/span><\/sub> \u540e\uff0c<\/span>m(t)<\/span><\/span> \u7a33\u5b9a\u5230\u4e00\u4e2a\u5438\u5f15\u5b50\u4e0a\uff0c\u5728\u76f8 III \u56f4\u7ed5\u96f6\u632f\u8361\uff0c\u5728\u76f8IV \u56f4\u7ed5\u4e00\u4e2a\u975e\u96f6\u503c\u632f\u8361\u3002\u56fe 4(a) \u7684\u63d2\u56fe\u5c55\u793a\u4e86 <\/span>m(t)<\/span><\/span> \u5bf9\u521d\u59cb\u6761\u4ef6\u5fae\u5c0f\u6270\u52a8\u7684\u654f\u611f\u6027\uff0c\u8fd9\u662f\u786e\u5b9a\u6027\u6df7\u6c8c\u7684\u7279\u5f81 [80]\u3002\u901a\u8fc7\u6c42\u89e3\u65b9\u7a0b (7) \u5e76\u6570\u503c\u8ba1\u7b97\u65f6\u95f4\u5e73\u5747\u503c [81]\u3002<\/span><\/span><\/section>\n

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\u5bf9\u4e8e<\/span><\/span>\"image.png\" <\/span><\/sub>\uff0c\u6211\u4eec\u4f30\u8ba1\u4e86\u754c\u5b9a\u76f8 IV \u7684\u76f8\u53d8\u7ebf [72]\u3002\u5bf9\u4e8e T<\/span>\u2192\u221e<\/span><\/span>\uff0c\u76f8 II \u548c\u76f8IV \u4e4b\u95f4\u7684\u76f8\u53d8\u7531 <\/span>\u0394<\/span><\/span> \u51b3\u5b9a\uff0c\u56e0\u4e3a\u5728\u4e0d\u52a8\u70b9\u76f8<\/span><\/span>\u0394 = 0\uff0c\u5728\u6df7\u6c8c\u76f8 <\/span>\u0394<\/span><\/span> > 0\u3002\u53c2\u6570 M \u533a\u5206\u4e86\u6df7\u6c8c\u76f8\uff1a\u5728\u76f8III \u4e2d M =  0\uff0c\u5728\u76f8 IV \u4e2d  M\u22600<\/span><\/span>\uff08\u89c1\u56fe 4\uff09<\/span><\/span>\u3002\u6211\u4eec\u5173\u4e8e\u76f8 III \u548c\u76f8 IV \u4e4b\u95f4\u76f8\u53d8\u7684\u6570\u503c\u7ed3\u679c\u4e0e\u56fe 2 \u4e2d\u7684\u865a\u7ebf\u4e00\u81f4\uff0c\u8fd9\u8868\u660e\u8fd9\u79cd\u76f8\u53d8\u7531\u7f51\u7edc\u8c31\u4e2d\u7684\u95f4\u9699 <\/span> |<\/span>\u03bb<\/span><\/span>1<\/span><\/sub><\/span>–<\/span>\u03bb<\/span><\/span>2<\/span><\/sub><\/span><\/span>| <\/span><\/span> \u63a7\u5236\u3002\u7136\u800c\uff0c\u5bf9\u4e8e c<\/span>\u2192\u221e<\/span><\/span>\uff0c\u5411\u6df7\u6c8c\u76f8 III \u7684\u8fd9\u79cd\u76f8\u53d8\u4e0e\u80fd\u9699 – \u65e0\u80fd\u9699\u8f6c\u53d8 [30] \u7565\u6709\u504f\u5dee\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u8f83\u5927\u7684 <\/span>\u03bc<\/span><\/span>J<\/span><\/sub>\u3002<\/span><\/span><\/section>\n

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\u7ed3\u8bba<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u6211\u4eec\u53d1\u5c55\u4e86\u7a00\u758f\u6709\u5411\u7f51\u7edc\u4e0a\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\uff0c\u63a8\u5bfc\u51fa\u4e86\u5728\u6781\u9650 <\/span>N\u2192\u221e<\/span><\/span> \u4e0b\u6709\u6548\u52a8\u529b\u5b66\u7684\u7cbe\u786e\u8def\u5f84\u6982\u7387\u65b9\u7a0b\u3002\u4e0e\u5177\u6709\u53cc\u5411\u8fb9\u7684\u7a00\u758f\u6a21\u578b [38, 39] \u4e0d\u540c\uff0c\u6211\u4eec\u7684\u8def\u5f84\u6982\u7387\u65b9\u7a0b\u53ef\u4ee5\u4f7f\u7528\u7fa4\u4f53\u52a8\u529b\u5b66\u8fdb\u884c\u6570\u503c\u6c42\u89e3 [64]\u3002\u901a\u8fc7\u4e0e\u6d41\u884c\u75c5\u4f20\u64ad\u3001\u795e\u7ecf\u7f51\u7edc\u548c\u751f\u6001\u7cfb\u7edf\u7814\u7a76\u4e2d\u57fa\u672c\u6a21\u578b\u7684\u6570\u503c\u6a21\u62df\u8fdb\u884c\u6bd4\u8f83\uff0c\u6211\u4eec\u9a8c\u8bc1\u4e86\u6211\u4eec\u4e00\u822c\u89e3\u7684\u7cbe\u786e\u6027\u3002\u6700\u540e\uff0c\u6211\u4eec\u5e94\u7528\u6211\u4eec\u7684\u89e3\u6765\u786e\u5b9a [1, 30] \u5178\u578b\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u7a00\u758f\u6709\u5411\u7248\u672c\u7684\u5b8c\u6574\u76f8\u56fe\u3002<\/span><\/span><\/section>\n

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\u56fe 4. \u5bf9\u4e8e\u5177\u6709\u6cca\u677e\u5165\u5ea6\u548c\u5747\u503c\u4e3a <\/span>\u03bc<\/span><\/span>J<\/span><\/sub> = 1\/3 \u7684\u9ad8\u65af\u5206\u5e03 p<\/span>J<\/span><\/sub> \u7684\u6709\u5411\u7f51\u7edc\uff0c\u5728\u6df7\u6c8c\u76f8\u5185 m(t) \u7684\u52a8\u529b\u5b66\u3002\u7ed3\u679c\u4f7f\u7528\u5177\u6709 <\/span>5\u00d710<\/span><\/span>4<\/span><\/sup> \u6761\u8def\u5f84\u548c\u591a\u4e2a\u521d\u59cb\u6761\u4ef6\u7684\u7fa4\u4f53\u52a8\u529b\u5b66\u5bf9\u516c\u5f0f (7) \u7684\u6c42\u89e3\u3002\u865a\u7ebf\u8868\u793a M \u7684\u503c\uff0c\u5373\u516c\u5f0f (11)\uff0c\u5b83\u8868\u5f81\u4e86\u6bcf\u4e2a\u76f8\u7684\u6df7\u6c8c\u5438\u5f15\u5b50\u3002(a) c = 2.5 \u548c <\/span>\u03c3<\/span><\/span>J<\/span><\/sub> = 2\u3002\u63d2\u56fe\uff1a\u4ece\u5355\u4e2a\u7f51\u7edc\u5b9e\u4f8b (N = 4000)\u3001\u521d\u59cb\u6761\u4ef6 x<\/span>i<\/span><\/sub>(0)  = 0.15 – \u03f5 \u548c\u4e0d\u540c\u7684 <\/span>\u03f5<\/span><\/span> \u7684\u786e\u5b9a\u6027\u516c\u5f0f (1) \u5f97\u5230 m(t) \u7684\u52a8\u529b\u5b66\u3002(b) c = 5 \u548c <\/span>\u03c3<\/span><\/span>J<\/span><\/sub>= 0.62\u3002<\/span><\/span><\/p>\n


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\u516c\u5f0f (7) \u7684\u6570\u503c\u89e3\u4e0d\u9700\u8981\u4ece\u914d\u7f6e\u6a21\u578b [71] \u751f\u6210\u7f51\u7edc\uff0c\u4e0e\u5728\u7f51\u7edc\u4e0a\u5bf9\u65b9\u7a0b (1) \u8fdb\u884c\u5927\u89c4\u6a21\u6a21\u62df [22] \u76f8\u6bd4\uff0c\u5177\u6709\u4e00\u5b9a\u7684\u8ba1\u7b97\u4f18\u52bf\u3002\u9664\u4e86\u5176\u6570\u503c\u5e94\u7528\u5916\uff0c\u516c\u5f0f (7) \u4e3a\u7814\u7a76\u7a33\u6001 [4]\u3001\u8ba1\u7b97\u5173\u8054\u51fd\u6570 [3]\u3001\u63a8\u5bfc\u5b8f\u89c2\u5e8f\u53c2\u91cf\u7684\u8fd1\u4f3c\u52a8\u529b\u5b66\u65b9\u7a0b\u4ee5\u53ca\u5f00\u53d1\u7cfb\u7edf\u7684\u5fae\u6270\u65b9\u6cd5 [26, 82] \u63d0\u4f9b\u4e86\u4e00\u4e2a\u57fa\u7840\u6846\u67b6\u3002<\/span><\/span><\/section>\n

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\u6211\u4eec\u7684\u5de5\u4f5c\u4e3a\u63a2\u7d22\u7a00\u758f\u5f02\u8d28\u7f51\u7edc\u5728\u751f\u6001\u7cfb\u7edf\u52a8\u529b\u5b66\u3001\u8026\u5408\u632f\u5b50\u3001\u6d41\u884c\u75c5\u4f20\u64ad\u7b49\u9886\u57df\u4e2d\u7684\u4f5c\u7528\u94fa\u5e73\u4e86\u9053\u8def\u3002\u672a\u6765\u7684\u5de5\u4f5c\u5305\u62ec\u786e\u5b9a\u7a00\u758f Lotka-Volterra \u6a21\u578b\u7684\u76f8\u56fe [7]\u3001\u5916\u90e8\u566a\u58f0\u5bf9\u76f8\u56fe\u7684\u5f71\u54cd [29] \u4ee5\u53ca\u7f51\u7edc\u5f02\u8d28\u6027\u5728\u590d\u6742\u7cfb\u7edf\u4e34\u754c\u6307\u6570 [77, 83] \u4e2d\u7684\u4f5c\u7528\u3002\u6700\u540e\uff0c\u5c06\u5f53\u524d\u7684\u5f62\u5f0f\u4f53\u7cfb\u4e0e\u6587\u732e [84] \u4e2d\u7684\u7a7a\u8154\u65b9\u6cd5\u8054\u7cfb\u8d77\u6765\u5c06\u662f\u5f88\u6709\u610f\u4e49\u7684\u3002<\/span><\/span><\/section>\n


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\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u8bfb\u4e66\u4f1a<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u4eba\u7c7b\u5927\u8111\u662f\u4e00\u4e2a\u7531\u6570\u4ee5\u767e\u4ebf\u8ba1\u7684\u795e\u7ecf\u5143\u76f8\u4e92\u8fde\u63a5\u6240\u6784\u6210\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u88ab\u8ba4\u4e3a\u662f\u300c\u5df2\u77e5\u5b87\u5b99\u4e2d\u6700\u590d\u6742\u7684\u7269\u4f53\u300d\u3002\u672c\u7740\u4fc3\u8fdb\u6765\u81ea\u795e\u7ecf\u79d1\u5b66\u3001\u7cfb\u7edf\u79d1\u5b66\u3001\u4fe1\u606f\u79d1\u5b66\u3001\u7269\u7406\u5b66\u3001\u6570\u5b66\u4ee5\u53ca\u8ba1\u7b97\u673a\u79d1\u5b66\u7b49\u4e0d\u540c\u9886\u57df\uff0c\u5bf9\u8111\u79d1\u5b66\u3001\u7c7b\u8111\u667a\u80fd\u4e0e\u8ba1\u7b97\u3001\u4eba\u5de5\u667a\u80fd\u611f\u5174\u8da3\u7684\u5b66\u672f\u5de5\u4f5c\u8005\u7684\u4ea4\u6d41\u4e0e\u5408\u4f5c\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u56fd\u5185\u5916\u591a\u6240\u77e5\u540d\u9ad8\u6821\u7684\u4e13\u5bb6\u5b66\u8005\u53d1\u8d77\u795e\u7ecf\u3001\u8ba4\u77e5\u3001\u667a\u80fd\u7cfb\u5217\u8bfb\u4e66\u4f1a\u7b2c\u4e09\u5b63\u2014\u2014\u300c\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u300d\u8bfb\u4e66\u4f1a<\/a>\uff0c\u6db5\u76d6\u590d\u6742\u795e\u7ecf\u52a8\u529b\u5b66\u3001\u795e\u7ecf\u5143\u5efa\u6a21\u4e0e\u8ba1\u7b97\u3001\u8de8\u5c3a\u5ea6\u795e\u7ecf\u52a8\u529b\u5b66\u3001\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u4e0eAI\u7684\u878d\u5408\u56db\u5927\u6a21\u5757\uff0c\u5e76\u5e0c\u671b\u63a2\u8ba8\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u5bf9\u7c7b\u8111\u667a\u80fd\u548c\u4eba\u5de5\u667a\u80fd\u7684\u542f\u53d1\u3002<\/span>\u8bfb\u4e66\u4f1a\u5df2\u5b8c\u7ed3\uff0c\u73b0\u5728\u62a5\u540d\u53ef\u52a0\u5165\u793e\u7fa4\u5e76\u89e3\u9501\u56de\u653e\u89c6\u9891\u6743\u9650\u3002<\/span><\/span><\/span><\/section>\n


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\"\u56fe\u7247\"<\/span><\/a><\/section>\n


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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/span>\u8ba1\u7b97\u795e\u7ecf\u79d1\u5b66\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1a\u4ece\u590d\u6742\u795e\u7ecf\u52a8\u529b\u5b66\u5230\u7c7b\u8111\u4eba\u5de5\u667a\u80fd<\/a><\/span><\/strong><\/p>\n


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\u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u8bfb\u4e66\u4f1a<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u96c6\u667a\u4ff1\u4e50\u90e8\u8054\u5408\u5408\u80a5\u5de5\u4e1a\u5927\u5b66\u7269\u7406\u7cfb\u6559\u6388\u674e\u660e\u3001\u540c\u6d4e\u5927\u5b66\u526f\u6559\u6388\u5f20\u6bc5\u8d85\u3001\u5317\u4eac\u5e08\u8303\u5927\u5b66\u7279\u8058\u526f\u7814\u7a76\u5458\u53f2\u8d35\u5143\u4e0e\u5728\u8bfb\u535a\u58eb\u751f\u90b1\u4ef2\u666e\u3001\u5f20\u7ae0\u5171\u540c\u53d1\u8d77<\/span><\/span>\u300c\u590d\u6742\u7f51\u7edc\u52a8\u529b\u5b66\u300d\u8bfb\u4e66\u4f1a<\/a><\/span>\u3002\u672c\u6b21\u8bfb\u4e66\u4f1a\u5c06\u63a2\u8ba8\uff1a\u540c\u6b65\u76f8\u53d8\u7684\u4e34\u754c\u6027\u3001\u5982\u4f55\u666e\u9002\u5730\u523b\u753b\u591a\u7a33\u6001\u4e0e\u4e34\u754c\u70b9\u3001\u5982\u4f55\u8bc6\u522b\u5e76\u9884\u6d4b\u4e34\u754c\u8f6c\u53d8\u3001\u5982\u4f55\u901a\u8fc7\u5c40\u90e8\u5e72\u9884\u6765\u8c03\u63a7\u7cfb\u7edf\u4fdd\u6301\u6216\u56de\u5230\u671f\u671b\u7a33\u6001\u3001\u7206\u70b8\u903e\u6e17\u4e34\u754c\u884c\u4e3a\u7684\u5173\u952e\u7279\u5f81\u3001\u4e0d\u540c\u7c7b\u578b\u7684\u7ea7\u8054\u8fc7\u7a0b\u5bf9\u903e\u6e17\u76f8\u53d8\u7684\u5f71\u54cd\u6709\u4f55\u5f02\u540c\u3001\u9ad8\u9636\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u80fd\u5426\u7b49\u6548\u4e3a\u82e5\u5e72\u7b80\u5355\u673a\u5236\u7684\u53e0\u52a0\u3001\u5982\u4f55\u6709\u6548\u5730\u4fc3\u8fdb\u4eba\u7c7b\u4e2a\u4f53\u95f4\u7684\u5408\u4f5c\u7b49\u95ee\u9898\u3002<\/span><\/span><\/section>\n

<\/span><\/span><\/section>\n
\u8bfb\u4e66\u4f1a\u8ba1\u5212\u4ece3\u67087\u65e5\u5f00\u59cb\uff0c\u6bcf\u5468\u4e94\u665a19:30-21:30\u8fdb\u884c\uff0c\u6301\u7eed8-10\u5468\u3002\u8bda\u631a\u9080\u8bf7\u9886\u57df\u5185\u7814\u7a76\u8005\u3001\u5bfb\u6c42\u8de8\u9886\u57df\u878d\u5408\u7684\u7814\u7a76\u8005\u52a0\u5165\uff0c\u5171\u540c\u63a2\u8ba8\u3002<\/span><\/span><\/section>\n


<\/span><\/span><\/p>\n

\"\u56fe\u7247\"<\/span><\/a><\/section>\n
\n


<\/span><\/span><\/p>\n

\u8be6\u60c5\u8bf7\u89c1\uff1a\u590d\u6742\u7f51\u7edc\u4e0a\u7684\u81ea\u7ec4\u7ec7\u4e0e\u96c6\u4f53\u884c\u4e3a\uff1a\u4ece\u6269\u6563\u3001\u76f8\u53d8\u5230\u535a\u5f08 | \u8bfb\u4e66\u4f1a\u542f\u52a8<\/a><\/span><\/span><\/p>\n<\/section>\n


<\/span><\/p>\n


<\/span><\/p>\n

\u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/section>\n
<\/strong><\/section>\n
1. <\/span><\/strong>\u590d\u6742\u7f51\u7edc\u4e2d\u7684\u52a8\u529b\u5b66\uff1a\u4ece\u7406\u8bba\u7a81\u7834\u5230\u5730\u7403\u751f\u6001\u7684\u8de8\u5b66\u79d1\u5bf9\u8bdd<\/a><\/span><\/strong><\/span><\/section>\n
2. <\/span><\/strong>PNAS \u901f\u9012\uff1a\u5177\u6709\u5fae\u89c2-\u5b8f\u89c2\u53cc\u5411\u56e0\u679c\u5173\u7cfb\u7684\u590d\u6742\u7cfb\u7edf\u52a8\u529b\u5b66\u7406\u8bba<\/a><\/span><\/strong><\/span><\/section>\n
3. <\/span><\/strong>Nat. Commun.\u524d\u6cbf\uff1a\u4ece\u5b9e\u9a8c\u6570\u636e\u4e2d\u5b66\u4e60\u53ef\u89e3\u91ca\u7684\u968f\u673a\u590d\u6742\u7cfb\u7edf\u52a8\u529b\u5b66<\/a><\/span><\/strong><\/span><\/section>\n
<\/strong><\/section>\n
4. <\/span><\/strong><\/span>\u6d8c\u73b0\u52a8\u529b\u5b66\u5982\u4f55\u7528\u6765\u5206\u6790\u590d\u6742\u7cfb\u7edf\uff1f | \u65b0\u8bfe\u4e0a\u7ebf<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
<\/strong>5. <\/span><\/strong>AI\u65f6\u4ee3\u7684\u5b66\u4e60\uff1a\u5171\u63a2\u4eba\u7c7b\u5b66\u4e60\u7684\u590d\u6742\u6027<\/span><\/a><\/span><\/strong><\/section>\n

6. <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/p>\n


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


<\/span><\/span><\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u8bb8\u591a\u73b0\u5b9e\u4e16\u754c\u7684\u590d\u6742\u7cfb\u7edf\u901a\u8fc7\u7a00\u758f\u5f02\u8d28\u7f51\u7edc\u76f8\u4e92\u4f5c\u7528\uff0c\u800c\u4f20\u7edf\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u5728\u5904\u7406\u8fd9\u7c7b\u7cfb\u7edf\u65f6\u5b58\u5728\u4e00\u5b9a\u5c40\u9650\u6027\u3002\u8fd9\u7bc7\u5de5\u4f5c\u9996\u6b21\u5c06\u52a8\u529b\u5b66\u5e73\u5747\u573a\u7406\u8bba\u6269\u5c55\u81f3\u7a00\u758f\u6709\u5411\u7f51\u7edc\uff0c\u63a8\u5bfc\u51fa\u5355\u81ea\u7531\u5ea6\u6709\u6548\u52a8\u529b\u5b66\u7684\u8def\u5f84\u6982\u7387\u7cbe\u786e\u65b9\u7a0b\u5e76\u5f00\u53d1\u9ad8\u6548\u6c42\u89e3\u7b97\u6cd5\u3002\u8fd9\u4e00\u7406\u8bba\u7a81\u7834\u5f25\u5408\u4e86\u7f51\u7edc\u7ed3\u6784\u4e0e\u7cfb\u7edf\u52a8\u529b\u5b66\u7814\u7a76\u95f4\u7684\u9e3f\u6c9f\uff0c\u5e76\u4e14\u8be5\u6846\u67b6\u5e7f\u6cdb\u9002\u7528\u4e8e\u795e\u7ecf\u7f51\u7edc…<\/p>\n","protected":false},"author":0,"featured_media":58367,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/58423"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=58423"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/58423\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/58367"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=58423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=58423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=58423"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=58423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}