{"id":18669,"date":"2020-03-11T20:39:43","date_gmt":"2020-03-11T12:39:43","guid":{"rendered":"https:\/\/swarma.org\/?p=18669"},"modified":"2020-03-13T14:00:57","modified_gmt":"2020-03-13T06:00:57","slug":"%e6%b7%b7%e6%b2%8c%e7%90%86%e8%ae%ba-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=18669","title":{"rendered":"\u6df7\u6c8c\u7406\u8bba | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u6df7\u6c8c\u8fb9\u7f18\uff08Edge of chaos\uff09\u662f\u4e00\u4e2a\u7528\u6765\u5f62\u5bb9\u7531\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u514b\u91cc\u65af\u6258\u5f17\u00b7\u6717\u987f\u53d1\u73b0\u7684\u73b0\u8c61\u3002\u6700\u5f00\u59cb\u8be5\u73b0\u8c61\u88ab\u7528\u6765\u63cf\u8ff0\u4e00\u4e2a\u53d8\u91cf\u03bb\u7684\u4e00\u6bb5\u53d6\u503c\u8303\u56f4\uff0c\u8be5\u53d8\u91cf\u662f\u4f5c\u4e3a\u7ec6\u80de\u81ea\u52a8\u673a\u7684\u4e00\u4e2a\u53c2\u6570\u3002\u5f53\u03bb\u53d8\u5316\uff0c\u7ec6\u80de\u81ea\u52a8\u673a\u7684\u884c\u4e3a\u4f1a\u4ea7\u751f\u76f8\u53d8\u3002\u514b\u91cc\u65af\u6258\u5f17\u00b7\u6717\u987f\uff08Christopher Langton)\u53d1\u73b0\u03bb\u7684\u67d0\u4e00\u5c0f\u6bb5\u53d6\u503c\u53ef\u4ee5\u4f7f\u7ec6\u80de\u81ea\u52a8\u673a\u5177\u6709\u901a\u7528\u8ba1\u7b97\u7684\u80fd\u529b\u3002\u6839\u636e\u03bb\u7684\u8fde\u7eed\u53d8\u5316\u80fd\u591f\u5f97\u5230\u56db\u79cd\u7ec6\u80de\u81ea\u52a8\u673a\u4e4b\u95f4\u7684\u8fc7\u6e21\u8f6c\u5316\u56fe\u666f\u5373\uff1a\u56fa\u5b9a\u70b9->\u5468\u671f->\u590d\u6742->\u6df7\u6c8c\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4\uff0c\u590d\u6742\u7684\u7ed3\u6784\u8bde\u751f\u4e8e\u6df7\u6c8c\u7684\u8fb9\u7f18\u3002<\/span><\/p>\n


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http:\/\/math.hws.edu\/eck\/js\/edge-of-chaos\/CA.html<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5438\u5f15\u5b50<\/strong>\uff08Attractor<\/strong>\uff09<\/strong><\/span><\/p>\n


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\u975e\u7ebf\u6027\u7cfb\u7edf\uff08Nonlinear System\uff09<\/strong><\/span><\/p>\n


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\u8d39\u6839\u9c8d\u59c6\u5e38\u6570 \uff08<\/strong>Feigenbaum Constants<\/strong>\uff09<\/strong><\/span><\/p>\n


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\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\uff08Feigenbaum Constants\uff09\u662f\u65b0\u8fd1\u53d1\u73b0\u7684\u3001\u4e14\u5728\u5b66\u672f\u754c\u8ba4\u5b9a\u7684\u4e00\u4e2a\u666e\u9002\u5e38\u6570\uff0c\u8fd9\u4e2a\u5e38\u6570\u4e0e\u201c\u6df7\u6c8c\u73b0\u8c61\u201d\u6709\u5173\u3002<\/span><\/section>\n

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\u56fe2\uff1a<\/span><\/strong>\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u56fe\u4f8b<\/span><\/strong><\/p>\n


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\u8774\u8776\u6548\u5e94\uff08Butterfly effect\uff09<\/strong><\/span><\/p>\n


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\u8774\u8776\u6548\u5e94\uff08Butterfly effect\uff09\u662f\u6307\u5bf9\u521d\u503c\u654f\u611f\u7684\u4e00\u7c7b\u6df7\u6c8c\u73b0\u8c61\u30021961\u5e74\u7f8e\u56fd\u6c14\u8c61\u5b66\u5bb6\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u5179\u5728\u6a21\u62df\u5927\u6c14\u4e2d\u7a7a\u6c14\u6d41\u52a8\u7684\u6570\u5b66\u6a21\u578b\uff0c\u5728\u8fdb\u884c\u7b2c\u4e8c\u6b21\u8ba1\u7b97\u65f6\uff0c\u76f4\u63a5\u8f93\u5165\u524d\u4e00\u6b21\u6a21\u62df\u7ed3\u679c\u7684\u6570\u636e\uff0c\u5374\u4e0e\u7b2c\u4e00\u6b21\u5b8c\u5168\u4e0d\u540c\uff0c\u68c0\u67e5\u540e\u53d1\u73b0\u662f\u56e0\u4e3a\u53d7\u9650\u4e8e\u8ba1\u7b97\u673a\u7684\u7cbe\u5ea6\uff0c\u5bfc\u81f4\u4e8c\u6b21\u8f93\u5165\u6570\u503c\u7684\u7cbe\u786e\u4f4d\u6570\u4e0d\u540c\uff0c\u540e\u6765\u4ed6\u5bf9\u8fd9\u4e00\u73b0\u8c61\u505a\u4e86\u7f1c\u5bc6\u7684\u63a8\u7406\u7814\u7a76\uff0c\u53d1\u8868\u7684\u201c\u786e\u5b9a\u6027\u975e\u5468\u671f\u6d41\u201d\u4e00\u6587\uff0c\u63ed\u793a\u4e86\u6df7\u6c8c\u7684\u521d\u503c\u654f\u611f\u7279\u6027\u3002<\/span><\/section>\n

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\u4e09\u4f53\u95ee\u9898\uff08Three-body Problem\uff09<\/strong><\/span><\/p>\n


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\u4e09\u4f53\u95ee\u9898\uff08Three-body Problem\uff09\u662f\u5929\u4f53\u529b\u5b66\u4e2d\u7684\u57fa\u672c\u529b\u5b66\u6a21\u578b\u3002\u5b83\u662f\u6307\u4e09\u4e2a\u8d28\u91cf\u3001\u521d\u59cb\u4f4d\u7f6e\u548c\u521d\u59cb\u901f\u5ea6\u90fd\u662f\u4efb\u610f\u7684\u53ef\u89c6\u4e3a\u8d28\u70b9\u7684\u5929\u4f53\uff0c\u5728\u76f8\u4e92\u4e4b\u95f4\u4e07\u6709\u5f15\u529b\u7684\u4f5c\u7528\u4e0b\u7684\u8fd0\u52a8\u89c4\u5f8b\u95ee\u9898\u3002<\/span><\/section>\n

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1887\u5e74\uff0c\u745e\u5178\u56fd\u738b\u5965\u65af\u5361\u4e8c\u4e16\u4e3a\u4e86\u795d\u8d3a\u81ea\u5df1\u768460\u5c81\u5bff\u8bde\u8d5e\u52a9\u4e86\u4e00\u9879\u7ade\u8d5b\uff0c\u5f81\u6c42\u592a\u9633\u7cfb\u7684\u7a33\u5b9a\u6027\u95ee\u9898\u7684\u89e3\u7b54\uff08\u4e09\u4f53\u95ee\u9898\u7684\u53d8\u5f0f\uff09\u3002\u6cd5\u56fd\u6570\u5b66\u5bb6\u5e9e\u52a0\u83b1\u6307\u51fa\u4e09\u4f53\u95ee\u9898\u4e0d\u80fd\u7cbe\u786e\u6c42\u89e3\uff0c\u6210\u4e86\u7b2c\u4e00\u4e2a\u53d1\u73b0\u6df7\u6c8c\u786e\u5b9a\u7cfb\u7edf\u7684\u4eba\uff0c\u5e76\u4e3a\u73b0\u4ee3\u7684\u6df7\u6c8c\u7406\u8bba\u6253\u4e0b\u4e86\u57fa\u7840\u3002<\/span><\/section>\n


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\u56fe3\uff1a\u4e09\u4f53\u95ee\u9898\u793a\u4f8b<\/span><\/strong><\/p>\n


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3. \u77e5\u540d\u5b66\u8005\u7b80\u4ecb<\/strong><\/section>\n<\/section>\n

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

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\u8a79\u59c6\u58eb\u00b7\u7ea6\u514b James A. Yorke<\/span><\/strong><\/span><\/p>\n


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\u56fe4\uff1a<\/strong>\u8a79\u59c6\u58eb\u00b7\u7ea6\u514b James A. Yorke<\/strong><\/strong><\/p>\n


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\u9a6c\u91cc\u5170\u5927\u5b66\u7269\u7406\u79d1\u6280\u6240\u6570\u5b66\u4e0e\u7269\u7406\u5b66\u6770\u51fa\u6821\u8058\u6559\u6388\uff0c\u7f8e\u56fd\u6570\u5b66\u5bb6\u548c\u7406\u8bba\u7269\u7406\u5b66\u5bb6\uff0c\u9a6c\u91cc\u5170\u5927\u5b66\u5b66\u9662\u5e02\u5206\u6821\u6570\u5b66\u548c\u7269\u7406\u548c\u6570\u5b66\u7cfb\u524d\u4efb\u7cfb\u4e3b\u4efb\u3002\u57281975\u5e74\u4e0e\u674e\u5929\u5ca9\u4e00\u540c\u53d1\u8868\u7684\u4e00\u7bc7\u9898\u4e3a\u300a\u5468\u671f\u4e09\u5219\u6df7\u6c8c\u300b\uff08Period Three Implies Chaos\uff09\u8bba\u6587\u4e2d\u521b\u9020\u4e86\u6df7\u6c8c\u8fd9\u4e2a\u6570\u5b66\u672f\u8bed\u3002<\/span><\/p>\n


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\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6 Mitchell J. Feigenbaum<\/span><\/strong><\/span><\/p>\n


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\u56fe5\uff1a<\/strong>\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6 Mitchell J. Feigenbaum<\/strong><\/strong><\/p>\n


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\u7f8e\u56fd\u6570\u5b66\u7269\u7406\u5b66\u5bb6\uff0c\u5eb7\u5948\u5c14\u5927\u5b66\u6559\u6388\uff0c\u6d1b\u514b\u83f2\u52d2\u5927\u5b66\u6559\u6388\uff0c\u6df7\u6c8c\u7406\u8bba\u7684\u5148\u9a71\uff0c\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u7684\u53d1\u73b0\u8005\uff0c1975\u5e748\u6708\uff0c\u4ed6\u5c31\u662f\u62ff\u7740\u8ba1\u7b97\u5668\u800c\u53d1\u73b0\u4e00\u4e2a\u548c\u6df7\u6c8c\u3001\u5355\u5cf0\u6620\u8c61\u7684\u5468\u671f\u70b9\u6709\u5173\u7684\u6570\uff0c\u5373\u540e\u6765\u7684\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\uff0c\u4e4b\u540e\u53d1\u73b0\u4e86\u5206\u6790\u5728\u5730\u56fe\u5b66\u7684\u5e94\u7528\u3002<\/span><\/section>\n


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\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7\u6d1b\u4f26\u5179 Edward Norton Lorenz<\/span><\/strong><\/span><\/p>\n


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\u56fe6\uff1a\u7231\u5fb7\u534e\u00b7\u8bfa\u987f\u00b7\u6d1b\u4f26\u5179 Edward Norton Lorenz<\/strong><\/p>\n


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\u7f8e\u56fd\u6570\u5b66\u4e0e\u6c14\u8c61\u5b66\u5bb6\u3002\u6df7\u6c8c\u7406\u8bba\u4e4b\u7236\uff0c\u8774\u8776\u6548\u5e94\u7684\u53d1\u73b0\u8005\u30021963\u5e74\u83b7\u7f8e\u56fd\u6c14\u8c61\u5b66\u4f1a\u8fc8\u8f9b\u683c\u5956\u3002<\/span><\/p>\n


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\u674e\u5929\u5ca9 Tien-Yien Li<\/span><\/strong><\/span><\/p>\n


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\u56fe7\uff1a\u674e\u5929\u5ca9 Tien-Yien Li<\/strong><\/p>\n


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\u751f\u4e8e\u4e2d\u56fd\u798f\u5efa\u7701\u7684\u7f8e\u7c4d\u6570\u5b66\u5bb6\uff0c\u5bc6\u6b47\u6839\u5dde\u7acb\u5927\u5b66\u6770\u51fa\u6570\u5b66\u6559\u6388\u30021974\u5e74\u5728\u9a6c\u91cc\u5170\u5927\u5b66\u53d6\u5f97\u535a\u58eb\u5b66\u4f4d\uff0c\u4ed6\u548c\u8a79\u59c6\u58eb\u00b7\u7ea6\u514b\u5408\u5199\u7684\u8bba\u6587\u300a\u5468\u671f\u4e09\u5219\u6df7\u6c8c\u300b\uff08Period Three Implies Chaos\uff09\uff0c\u662f\u6df7\u6c8c\u52a8\u529b\u7cfb\u7edf\u7684\u91cd\u8981\u8bba\u6587\u3002\u8fd9\u4e2a\u7814\u7a76\u7ed3\u679c\u662f\u6c99\u53ef\u592b\u65af\u57fa\u5b9a\u7406\uff08Sharkovskii’s theorem\uff09\u7684\u7279\u6b8a\u60c5\u51b5\u3002<\/span><\/p>\n


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

\u9648\u5173\u8363 Guanrong Chen<\/span><\/strong><\/span><\/p>\n


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

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\u56fe8\uff1a\u9648\u5173\u8363 Guanrong Chen<\/strong><\/p>\n


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\u9999\u6e2f\u57ce\u5e02\u5927\u5b66\u6559\u6388\uff0c\u56fd\u5185\u5916\u591a\u6240\u77e5\u540d\u5927\u5b66\u5ba2\u5ea7\u6559\u6388\u3002\u5728\u6df7\u6c8c\u63a7\u5236\u53ca\u5206\u5c94\u7406\u8bba\u5206\u6790\u4e0e\u5e94\u7528\u65b9\u9762\u505a\u51fa\u5960\u57fa\u6027\u8d21\u732e\u800c\u88ab\u9009\u4e3a\u56fd\u9645\u7535\u5b50\u5de5\u7a0b\u5b66\u4f1a(IEEE) Fellow\u3002<\/span><\/p>\n


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5.\u76f8\u5173\u8d44\u6e90\u63a8\u8350<\/strong>
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\u6df7\u6c8c\u4e0e\u5206\u5f62\uff1a\u7b80\u4ecb <\/strong><\/span><\/p>\n

Chaos and Fractals: An Elementary Introduction<\/em><\/p>\n

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\u8fd9\u672c\u4e66\u4e3a\u8bfb\u8005\u63d0\u4f9b\u4e86\u5bf9\u6df7\u6c8c\u548c\u5206\u5f62\u7684\u57fa\u672c\u4ecb\u7ecd\uff0c\u9002\u5408\u6ca1\u6709\u5b66\u4e60\u5fae\u79ef\u5206\u6216\u7269\u7406\u5b66\u4f46\u5177\u6709\u521d\u7b49\u4ee3\u6570\u80cc\u666f\u7684\u5b66\u751f\u3002\u6b64\u4e66\u901a\u8fc7\u7b80\u5355\u8fed\u4ee3\u51fd\u6570\u4ecb\u7ecd\u4e86\u6df7\u6c8c\u7684\u91cd\u8981\u73b0\u8c61\u2014\u2014\u975e\u5468\u671f\u6027\u3001\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u3001\u5206\u5c94\u73b0\u8c61\u3002\u672c\u4e66\u8fd8\u9610\u91ca\u4e86\u4e8c\u7ef4\u52a8\u529b\u7cfb\u7edf\uff0c\u5947\u5f02\u5438\u5f15\u5b50\uff0c\u5143\u80de\u81ea\u52a8\u673a\uff0c\u548c\u6df7\u6c8c\u5fae\u5206\u65b9\u7a0b\u7b49\u6982\u5ff5\u3002<\/span><\/p>\n<\/section>\n


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\u6df7\u6c8c\u4e0e\u5206\u5f62\uff1a\u7b80\u4ecb<\/span><\/p>\n

Chaos and Fractals: An Elementary Introduction<\/span><\/p>\n

http:\/\/rrd.me\/gr3Cq<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6df7\u6c8c\u4e0e\u5206\u5f62 <\/strong><\/span>Chaos and Fractals<\/em><\/p>\n


\u8fd9\u672c\u4e66\u7684\u5341\u56db\u4e2a\u7ae0\u8282\u6db5\u76d6\u4e86\u6df7\u6c8c\u548c\u5206\u5f62\u7684\u4e2d\u5fc3\u601d\u60f3\u548c\u6982\u5ff5\uff0c\u4ee5\u53ca\u8bb8\u591a\u76f8\u5173\u7684\u4e3b\u9898\u5982\uff1a\u5206\u5f62\u4e0e\u81ea\u76f8\u4f3c\u3001\u5206\u5f62\u7684\u7ef4\u6570\u4e0e\u6d4b\u5ea6\u3001\u7ec6\u80de\u5143\u81ea\u52a8\u673a\u4e0e\u5438\u5f15\u5b50\u3001\u5206\u5f62\u6784\u9020\u4e2d\u7684\u968f\u673a\u6027\u3001\u786e\u5b9a\u6027\u6df7\u6c8c\u3001\u7075\u654f\u5ea6\u3001\u6df7\u5408\u4e0e\u5468\u671f\u70b9\u3001\u6709\u5e8f\u4e0e\u6df7\u6c8c\u3001\u5947\u5f02\u5438\u5f15\u5b50\u7b49\uff0c\u91cd\u70b9\u4ecb\u7ecd\u4e86\u5206\u5f62\u4e0e\u6df7\u6c8c\u7684\u7269\u7406\u610f\u4e49\u3001\u4e24\u8005\u4e4b\u95f4\u7684\u5173\u7cfb\u3001\u4e0e\u6570\u5b66\u7684\u5176\u5b83\u65b9\u9762\u4ee5\u53ca\u81ea\u7136\u73b0\u8c61\u7684\u8054\u7cfb\u3002<\/span><\/p>\n


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\u6df7\u6c8c\u4e0e\u5206\u5f62 Chaos and Fractals <\/span><\/p>\n

http:\/\/rrd.me\/gr3Jn<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6df7\u6c8c\u4e0e\u65f6\u95f4\u5e8f\u5217\u5206\u6790<\/strong><\/span> <\/p>\n

Chaos and Time-series Analysis<\/em><\/p>\n


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\u6b64\u4e66\u4ecb\u7ecd\u6df7\u6c8c\u7684\u53d1\u5c55\u548c\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u6709\u5173\u4e3b\u9898\u5185\u5bb9\uff0c\u5305\u62ec\u68c0\u6d4b\u548c\u5b9e\u9a8c\u6570\u636e\u4e2d\u7684\u6df7\u6c8c\u91cf\u5316\uff0c\u5206\u5f62\u548c\u590d\u6742\u7cfb\u7edf\u3002\u6d89\u53ca\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7edd\u5927\u591a\u6570\u91cd\u8981\u7684\u57fa\u672c\u6982\u5ff5\uff0c\u91cd\u70b9\u9610\u8ff0\u4e86\u7269\u7406\u6982\u5ff5\u548c\u6548\u7528\u7ed3\u679c\uff0c\u800c\u4e0d\u662f\u5728\u6570\u5b66\u4e0a\u8fdb\u884c\u8bc1\u660e\u548c\u63a8\u5bfc\u3002<\/span><\/p>\n


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\u6df7\u6c8c\u4e0e\u65f6\u95f4\u5e8f\u5217\u5206\u6790 <\/span><\/p>\n

Chaos and Time-series Analysis<\/span><\/p>\n

http:\/\/rrd.me\/gr3KC<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6df7\u6c8c\uff1a\u521b\u9020\u65b0\u7684\u79d1\u5b66<\/strong><\/span> <\/em><\/p>\n

Chaos: Making a new science<\/em><\/p>\n


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\u672c\u4e66\u5e76\u6ca1\u6709\u5c1d\u8bd5\u53bb\u89e3\u91caJulia\u96c6\u5408\u3001\u6d1b\u4f26\u5179\u5438\u5f15\u5b50\u548c\u5e9e\u5927\u590d\u6742\u7684Mandelbort\u96c6\u5408\uff0c\u800c\u662f\u4f9d\u9760\u8349\u56fe\u3001\u7167\u7247\u548c\u4f5c\u8005\u7cbe\u5f69\u7684\u63cf\u8ff0\u6027\u6563\u6587\u6765\u6784\u6210\u4e86\u6574\u672c\u4e66\u7684\u5185\u5bb9\u3002\u5728\u672c\u4e66\u4e2d\u8bfb\u8005\u4f1a\u9047\u5230\u8bb8\u591a\u975e\u51e1\u800c\u53c8\u53e4\u7075\u7cbe\u602a\u7684\u4eba\u3002\u4f8b\u5982\uff0c\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6 Mitchell J. Feigenbaum\uff0c\u4ed6\u7528\u4e00\u4e2a26\u5c0f\u65f6\u7684\u65f6\u949f\u6784\u5efa\u548c\u8c03\u6574\u81ea\u5df1\u7684\u751f\u6d3b\uff0c\u5e76\u4e14\u89c2\u5bdf\u4ed6\u9192\u7740\u7684\u65f6\u95f4\u4e0e\u4ed6\u5728\u6d1b\u65af\u963f\u62c9\u83ab\u65af\u56fd\u5bb6\u5b9e\u9a8c\u5ba4\u7684\u540c\u4e8b\u7684\u65f6\u95f4\u662f\u5426\u76f8\u540c\u3002<\/span><\/p>\n


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\u6df7\u6c8c\uff1a\u521b\u9020\u65b0\u7684\u79d1\u5b66 <\/span><\/p>\n

Chaos: Making a new science <\/span><\/p>\n

http:\/\/rrd.me\/gr3L7<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u6d8c\u73b0\uff1a\u4ece\u6df7\u6c8c\u5230\u6709\u5e8f<\/strong><\/span> <\/p>\n

Emergence: From Chaos to Order<\/em>
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\u672c\u4e66\u4f5c\u8005\u7ea6\u7ff0\u00b7\u970d\u5170\u5fb7\uff08John H. Holland\uff09\u662f\u5f53\u4eca\u6700\u5177\u6709\u521b\u65b0\u610f\u8bc6\u7684\u601d\u60f3\u5bb6\u4e4b\u4e00\uff0c\u5728\u672c\u4e66\u4e2d\uff0c\u4f5c\u8005\u6bd4\u8f83\u4e86\u663e\u793a\u6d8c\u73b0\u73b0\u8c61\u7684\u4e0d\u540c\u7cfb\u7edf\u548c\u6a21\u578b\uff0c\u5c55\u73b0\u4e86\u5b83\u4eec\u4e4b\u95f4\u5171\u540c\u7684\u89c4\u5219\u6216\u89c4\u5f8b\uff0c\u8bb2\u8ff0\u4e86\u4ece\u201c\u8574\u542b\u7740\u89c4\u8303\u3001\u80fd\u591f\u751f\u6210\u50cf\u5de8\u5927\u7684\u7ea2\u6749\u548c\u666e\u901a\u7684\u96cf\u83ca\u90a3\u6837\u590d\u6742\u800c\u72ec\u7279\u7ed3\u6784\u201d\u7684\u5fae\u5c0f\u79cd\u5b50\uff0c\u5230\u80fd\u591f\u901a\u8fc7\u81ea\u5b66\u4e60\u5728\u897f\u6d0b\u8df3\u68cb\u6e38\u620f\u4e2d\u8ba9\u8bbe\u8ba1\u8005\u4e00\u8d25\u6d82\u5730\u7684\u8ba1\u7b97\u673a\uff1b\u4ece\u80fd\u591f\u4fee\u5efa\u6865\u6881\u3001\u8de8\u8d8a\u6df1\u6c9f\u548c\u9a7e\u9a6d\u6811\u53f6\u4e4b\u821f\u5728\u6eaa\u6d41\u4e0a\u822a\u884c\u7684\u8681\u7fa4\uff0c\u5230\u8bd7\u4eba\u5145\u6ee1\u611f\u60c5\u7684\u521b\u4f5c\u7b49\u6d8c\u73b0\u73b0\u8c61\u7684\u5177\u4f53\u8868\u73b0\u3002<\/span><\/p>\n


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\u6d8c\u73b0\uff1a\u4ece\u6df7\u6c8c\u5230\u6709\u5e8f <\/span><\/p>\n

Emergence: From Chaos to Order
<\/span><\/p>\n

http:\/\/rrd.me\/grAGC<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u8bfe\u7a0b\uff1a<\/strong><\/span><\/p>\n


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\u590d\u6742\u6027\u601d\u7ef4\uff1a\u4ece\u6df7\u6c8c\u5f00\u59cb<\/strong><\/span>
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\u590d\u6742\u6027\u601d\u7ef4\uff1a\u4ece\u6df7\u6c8c\u5f00\u59cb 
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https:\/\/campus.swarma.org\/play\/coursedetail?id=11137<\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u5176\u4ed6\u63a8\u8350\uff1a<\/strong><\/span><\/p>\n


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\u5c0f\u8bf4<\/strong>\uff1a\u5218\u6148\u6b23 \u300a\u4e09\u4f53\u300b<\/span><\/p>\n


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\u7535\u5f71<\/span><\/strong>\uff1a\u300a\u8774\u8776\u6548\u5e94\u300b \u3001\u300a\u7f57\u62c9\u5feb\u8dd1\u300b<\/span><\/p>\n


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\u8bb0\u5f55\u7247<\/span><\/strong>\uff1a\u795e\u79d8\u7684\u6df7\u6c8c\u7406\u8bba Documentary: The mysterious theory of chaos<\/span><\/p>\n


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\u3010\u7eaa\u5f55\u7247\u3011\u795e\u79d8\u7684\u6df7\u6c8c\u7406\u8bba The Secret Life of Chaos 2009\uff08\u4e2d\u6587\u5b57\u5e55\uff09<\/span><\/h1>\n

https:\/\/www.bilibili.com\/video\/av24640476?from=search&seid=14892928752614783207<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u4ee5\u4e0a\u5185\u5bb9\u90fd\u662f\u6211\u4eec\u505a\u8fd9\u9879\u76ee\u7684\u8d77\u70b9\uff0c\u4f5c\u4e3a\u6765\u81ea\u4e0d\u540c\u5b66\u79d1\u548c\u9886\u57df\u7684\u5fd7\u613f\u8005\uff0c\u6211\u4eec\u5efa\u7acb\u8d77\u4e00\u4e2a\u6709\u6548\u7684\u767e\u79d1\u56e2\u961f\uff0c\u5206\u914d\u6709\u5ba1\u6821\u3001\u7ffb\u8bd1\u3001\u7f16\u8f91\u3001\u5ba3\u4f20\u7b49\u5de5\u4f5c\u3002\u6211\u4eec\u79c9\u6301\uff1a\u77e5\u8bc6\u4ece\u6211\u800c\u6765\uff0c\u95ee\u9898\u5230\u6211\u4e3a\u6b62<\/strong>\u7684\u4fe1\u5ff5\uff0c\u8ba4\u771f\u8d1f\u8d23\u7f16\u64b0\u6bcf\u4e00\u4e2a\u8bcd\u6761\u3002<\/span><\/p>\n


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<\/span>\u5728\u8fd9\u91cc<\/span>\u4ece\u590d\u6742\u6027<\/span>\u77e5\u8bc6\u51fa<\/span>\u53d1<\/span>\u4e0e<\/span>\u4f19\u4f34\u540c\u884c<\/span>\uff0c<\/span>\u540c\u65f6\u6211\u4eec\u5e0c\u671b\u6709\u66f4\u591a\u5fd7\u613f\u8005\u52a0\u5165\u8fd9\u4e2a\u56e2\u961f\uff0c\u4f7f\u767e\u79d1\u8bcd\u6761\u5185\u5bb9\u5f97\u5230\u6269\u5145\uff0c\u5e76\u4e3a\u6bcf\u4f4d\u5fd7\u613f\u8005\u63d0\u4f9b\u76f8\u5e94\u5956\u52b1\u4e0e\u8d44\u6e90\uff0c\u5efa\u7acb\u4e2a\u4eba\u4e3b\u9875\u4e0e\u8d21\u732e\u8bb0\u5f55\uff0c\u4f7f\u5176\u80fd\u591f\u7ee7\u7eed\u63a2\u7d22\u590d\u6742\u4e16\u754c\u3002<\/span><\/p>\n


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\u4f5c\u4e3a\u767e\u79d1\u9879\u76ee\u5fd7\u613f\u8005\uff0c\u5e0c\u671b\u4f60\u80fd\u5728\u5174\u8da3\u9a71\u52a8\u4e0b\uff0c\u627e\u5230\u5bf9\u5e94\u5185\u5bb9\uff0c\u4f7f\u5176\u53d8\u6210\u4e00\u4e2a\u53ef\u88ab\u5927\u5bb6\u5e7f\u6cdb\u5b66\u4e60\u79d1\u5b66\u8bcd\u6761\u3002\u4e0a\u8ff0\u5f85\u5efa\u7acb\u8bcd\u6761\u5171\u8ba115\u6761\uff0c<\/span>\u5982\u679c\u5927\u5bb6\u6709\u610f\u613f\u53c2\u4e0e\u8fd9\u4e2a\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u8bf7\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u6dfb\u52a0\u6211\u4eec\u7684\u8d1f\u8d23\u4eba\u3002<\/span><\/p>\n

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\u53c2\u8003\u8d44\u6599<\/strong>\uff1a<\/strong><\/p>\n


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[1]\u5438\u5f15\u5b50  \u7ef4\u57fa\u767e\u79d1 :<\/span><\/strong><\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Attractorm<\/span><\/strong><\/span><\/p>\n

[2]\u6df7\u6c8c\u8fb9\u7f18 \u7ef4\u57fa\u767e\u79d1:<\/span><\/strong><\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Edge_of_chaos<\/span><\/strong><\/span><\/p>\n

[3]\u975e\u7ebf\u6027\u7cfb\u7edf \u767e\u5ea6\u767e\u79d1 :<\/span><\/strong><\/span><\/p>\n

https:\/\/baike.baidu.com\/item\/%E9%9D%9E%E7%BA%BF%E6%80%A7%E7%B3%BB%E7%BB%9F\/354475?fr=aladdin<\/span><\/strong><\/span><\/p>\n

[4] \u8d39<\/span><\/strong><\/span>\u6839\u9c8d\u59c6\u5e38\u6570 \u7ef4\u57fa\u767e\u79d1<\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Feigenbaum_constants <\/span><\/strong><\/span><\/p>\n

[5] <\/span><\/strong><\/span>Logistic Map \u7ef4\u57fa\u767e\u79d1<\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Logistic_map<\/span><\/strong><\/span><\/strong><\/p>\n

[6]\u4e09\u4f53\u95ee\u9898\uff0c\u7ef4\u57fa\u767e\u79d1<\/span><\/strong><\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Three-body_problem<\/span><\/strong><\/span><\/p>\n

[7] \u8774\u8776\u6548\u5e94 \u7ef4\u57fa\u767e\u79d1<\/span><\/strong><\/span><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Butterfly_effect<\/span><\/strong><\/span><\/strong><\/p>\n

[8] \u6df7\u6c8c\u8fb9\u7f18 <\/span><\/strong><\/span><\/strong><\/span><\/p>\n

http:\/\/math.hws.edu\/eck\/js\/edge-of-chaos\/CA.html<\/span><\/strong><\/span><\/p>\n


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\u53c2\u8003\u8d44\u6599\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b<\/p>\n<\/section>\n<\/section>\n


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\u6765\u6e90\uff1a\u96c6\u667a\u767e\u79d1<\/span><\/section>\n
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\u63a8\u8350\u9605\u8bfb<\/strong><\/span><\/p>\n

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\u4ec0\u4e48\u662f\u5143\u80de\u81ea\u52a8\u673a\uff1f| \u96c6\u667a\u767e\u79d1<\/span><\/strong><\/a><\/strong><\/section>\n
\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u548c\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u7684\u5468\u671f\u6027<\/span><\/strong><\/strong><\/a>
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\u4e0d\u7528\u7e41\u7410\u516c\u5f0f\uff0c\u5982\u4f55\u9884\u6d4b\u590d\u6742\u7684\u6df7\u6c8c\u7cfb\u7edf\uff1f<\/span><\/strong><\/strong><\/a>
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\u4e00\u5802\u8bfe\u8bb2\u6e05\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u3001\u6df7\u6c8c\u3001\u5206\u578b\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u590d\u6742\u7cfb\u7edf\u7684\u533a\u522b\u548c\u8054\u7cfb<\/a><\/span><\/strong><\/strong><\/section>\n
\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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\u96c6\u667a\u4ff1\u4e50\u90e8QQ\u7fa4\uff5c877391004<\/span><\/strong><\/p>\n

\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org
<\/span><\/strong><\/p>\n

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\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n


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\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

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\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u672c\u7bc7\u6587\u7ae0\u6765\u6e90\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7: \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u201c\u96c6\u667a\u767e\u79d1\u7cbe\u9009\u201d\u662f\u4e00\u4e2a\u957f\u671f\u4e13\u680f\uff0c\u6301\u7eed\u4e3a\u5927\u5bb6\u63a8\u9001\u590d\u6742\u6027\u79d1\u5b66\u76f8\u5173\u7684\u57fa\u672c\u6982\u5ff5\u548c\u8d44\u6e90\u4fe1\u606f\u3002\u4f5c\u4e3a\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u5f00\u6e90\u79d1\u5b66\u9879\u76ee\uff0c\u96c6\u667a\u767e\u79d1\u5e0c\u671b\u6253\u9020\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u6700\u5168\u9762\u7684\u767e\u79d1\u5168\u4e66\uff0c\u6b22\u8fce\u5bf9\u590d\u6742\u6027\u79d1\u5b66\u611f\u5174\u8da3\u3001\u70ed\u7231\u77e5\u8bc6\u6574\u7406\u548c\u5206\u4eab\u7684\u670b\u53cb\u52a0\u5165\uff01 \u4eca\u5929\u5206\u4eab\u590d\u6742\u6027\u79d1\u5b66\u9886\u57df\u91cc\u9762\u4e00\u4e2a\u975e\u5e38\u672c\u8d28\u7684\u7406\u8bba\uff1a\u6df7\u6c8c\u7406\u8bba\u3002\u672c\u6587\u5c06\u4ecb\u7ecd\u6df7\u6c8c\u7406\u8bba\u7684\u57fa\u672c\u6982\u5ff5…<\/p>\n","protected":false},"author":1,"featured_media":18657,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[28],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/18669"}],"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"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=18669"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/18669\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/18657"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=18669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=18669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=18669"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=18669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}