{"id":12060,"date":"2018-10-14T01:00:00","date_gmt":"2018-10-13T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%e4%b8%80%e5%a0%82%e8%af%be%e8%ae%b2%e6%b8%85%e9%9d%9e%e7%ba%bf%e6%80%a7%e5%8a%a8%e5%8a%9b%e5%ad%a6%e3%80%81%e6%b7%b7%e6%b2%8c%e3%80%81%e5%88%86%e5%9e%8b%e3%80%81%e7%bd%91%e7%bb%9c%e7%a7%91%e5%ad%a6-2\/"},"modified":"2019-01-03T10:07:49","modified_gmt":"2019-01-03T02:07:49","slug":"%e4%b8%80%e5%a0%82%e8%af%be%e8%ae%b2%e6%b8%85%e9%9d%9e%e7%ba%bf%e6%80%a7%e5%8a%a8%e5%8a%9b%e5%ad%a6%e3%80%81%e6%b7%b7%e6%b2%8c%e3%80%81%e5%88%86%e5%9e%8b%e3%80%81%e7%bd%91%e7%bb%9c%e7%a7%91%e5%ad%a6-2","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=12060","title":{"rendered":"\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"},"content":{"rendered":"
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<\/section>\n

\"\u96c6\u667a\"<\/p>\n

\n

\u5982\u679c\u4f60\u548c\u6211\u4e00\u6837\uff0c\u5bf9\u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff08Nonlinear Dynamics\uff09\u3001\u6df7\u6c8c\uff08Chaos\uff09\u3001\u5206\u5f62\uff08Fractals\uff09\u3001\u7f51\u7edc\u79d1\u5b66\uff08Network Science\uff09\u3001\u590d\u6742\u7cfb\u7edf\uff08Complex Systems\uff09\u611f\u5174\u8da3\uff0c<\/strong>\u4f46\u662f\u6709\u65f6\u5019\u5374\u89c9\u5f97\u4ed6\u4eec\u90fd\u5dee\u4e0d\u591a\u662f\u4e00\u56de\u4e8b\uff0c\u641e\u4e0d\u6e05\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u90a3\u4e48\u8fd9\u5802Strogatz\u6559\u6388\u7684\u8bfe\u4e0d\u4ec5\u53ef\u4ee5\u544a\u8bc9\u6211\u4eec\u8fd9\u4e9b\u6982\u5ff5\u662f\u4ec0\u4e48\u610f\u601d\uff0c\u8fd8\u53ef\u4ee5\u4ece\u5386\u53f2\u89d2\u5ea6\u4ecb\u7ecd\u4ed6\u4eec\u7684\u53d1\u5c55\uff0c\u4ee5\u53ca\u6570\u5b66\u4e0a\u4ed6\u4eec\u4e4b\u95f4\u7684\u660e\u786e\u8054\u7cfb\u3002<\/span><\/p>\n

\n

\u90a3\u4e48\u8c01\u662fStrogatz\u6559\u6388\u5462\uff1f<\/span><\/strong>\u67d0\u5356\u4e66\u7684\u7f51\u7ad9\u4e0a\u5bf9Strogatz\u6559\u6388\u7684\u4ecb\u7ecd\u662f\u8fd9\u6837\u7684\uff1a<\/span><\/p>\n

\n

Steven H. Strogatz\uff0c\u7f8e\u56fd\u827a\u672f\u4e0e\u79d1\u5b66\u9662\u9662\u58eb\uff0c\u5eb7\u5948\u5c14\u5927\u5b66\u5e94\u7528\u6570\u5b66\u7cfb Schurman \u6559\u6388\uff0c\u56fd\u9645\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e13\u5bb6\uff0c\u4e3b\u8981\u7814\u7a76\u9886\u57df\u662f\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u590d\u6742\u7cfb\u7edf\uff0c<\/strong>\u76ee\u524d\u5df2\u53d1\u8868\u8bba\u6587200\u591a\u7bc7\uff0c\u5176\u8457\u4f5c\u88ab\u5f15\u7528\u6b21\u6570\u8fbe\u523016300\u591a\u6b21\u3002<\/span><\/p>\n

\n

Strogatz\u6559\u6388\u66fe\u83b7\u5f97\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u9ad8\u6559\u5b66\u5956\u4ee5\u53ca\u6570\u5b66\u666e\u53ca\u7ec8\u8eab\u6210\u5c31\u5956\u7b49\u8363\u8a89\uff0c\u4ed6\u7684\u5173\u4e8e\u591a\u79cd\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7814\u7a76\u5df2\u88ab Scientific American,Nature, Discover, Business Week \u4ee5\u53ca The New York Times \u7b49\u4f5c\u4e3a\u7279\u8f91\u62a5\u5bfc\u3002<\/span><\/p>\n

\n

\u662f\u4e0d\u662f\u89c9\u5f97\u5f88\u725b\u903c\u4f46\u7136\u5e76\u5375\uff0c\u90a3\u6211\u53ea\u80fd\u8bb2\u5927\u5bb6\u719f\u6089\u7684\u4e00\u4ef6\u4e8b\u4e86\uff1a<\/span><\/strong><\/p>\n

\n

\u5f53Watts\u63d0\u51fa\u8457\u540d\u7684\u201c\u516d\u5ea6\u7406\u8bba\u201d\u5f15\u7206\u793e\u4ea4\u7f51\u7edc\u7684\u65f6\u5019\uff0c\u4ed6\u662f\u57fa\u4e8e\u81ea\u5df1\u57281998\u5e74\u53d1\u8868\u7684\u4e00\u7bc7Nature\u8bba\u6587\u300aCollective dynamics of ‘small-world’ networks\u300b\u3002<\/strong>\u90a3\u65f6Strogatz\u662fWatts\u7684\u5bfc\u5e08\uff0c\u8fd9\u7bc7\u8bba\u6587\u7684\u7b2c\u4e8c\u4f5c\u8005\u3002\u8fd9\u7bc7\u8bba\u6587\u7684\u5f15\u7528\u91cf\u662f37257\uff0c\u7269\u7406\u5b66\u9886\u57df\u6240\u6709\u8bba\u6587\u6309\u5f15\u7528\u91cf\u6392\u540d\u7b2c\u516d\u3002<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u4ed6\u7684\u7b11\u5bb9<\/span><\/strong><\/p>\n

\n

\u8fdb\u4e00\u6b65\u4e86\u89e3\u4ed6\uff0c\u53ef\u4ee5\u8bbf\u95ee\u4e2a\u4eba\u4e3b\u9875\uff1ahttp:\/\/www.stevenstrogatz.com\/<\/span><\/p>\n

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\n

\n

\u8fd9\u95e8\u8bfe\u662f\u5eb7\u5948\u5c14\u5927\u5b66\u7684MAE 5790\uff0c\u770b\u7f16\u53f7\u53ef\u4ee5\u77e5\u9053\uff0c\u8fd9\u662f\u673a\u68b0\u4e0e\u822a\u7a7a\u822a\u5929\u5de5\u7a0b\u5b66\u9662\uff08MAE\uff09\u7684\u4e00\u95e8\u7814\u7a76\u751f\u4e00\u5e74\u7ea7\u7ea7\u522b\u7684\u8bfe\u7a0b\uff085XXX\uff09\u3002\u8bfe\u7a0b\u540d\u79f0\uff1aNonlinear dynamics and chaos\u3002<\/span><\/p>\n

\n

\n

\u8bfe\u7a0b\u89c6\u9891\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/www.youtube.com\/watch?v=ycJEoqmQvwg&feature=youtu.be<\/span><\/p>\n<\/blockquote>\n

\n

\u5982\u679c\u4f60\u73b0\u5728\u80fd\u6324\u51fa\u4e00\u4e2a\u534a\u5c0f\u65f6\uff0c\u6211\u5efa\u8bae\u76f4\u63a5\u70b9\u5f00\u8fd9\u95e8\u8bfe\u7684\u7b2c\u4e00\u5802\u6982\u8ff0\u8bfe\uff0c\u542cStrogatz\u6559\u6388\u672c\u4eba\u8ddf\u4f60\u5a13\u5a13\u9053\u6765\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u89c6\u9891\uff1a\u4ed6\u7684\u7b2c\u4e00\u8bfe<\/span><\/strong><\/p>\n

\n

\u5982\u679c\u6682\u65f6\u6ca1\u7a7a\uff0c\u90a3\u4e48\u8bf7\u8ba9\u5fae\u81e3\u5e2e\u5fd9\u603b\u7ed3\u4e00\u4e0b\u3002\u540e\u9762\u7684\u5185\u5bb9\u7ea610\u5206\u949f\u8bfb\u5b8c\u3002<\/span><\/p>\n

\n

\u4e3a\u4e86\u914d\u5408\u8fd9\u95e8\u8bfe\uff0cStrogatz\u6559\u6388\u5199\u4e86\u4e00\u672c\u540c\u540d\u6559\u6750\uff0c\u73b0\u5728\u662f\u7b2c\u4e8c\u7248\u3002\uff08\u6709\u4e2d\u6587\u7248\uff0c\u4f46\u636e\u8bf4\u7ffb\u8bd1\u4e0d\u5730\u9053\uff0c\u6709\u57fa\u7840\u7684\u540c\u5b66\u5efa\u8bae\u76f4\u63a5\u8bfb\u539f\u7248\uff09<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

Nonlinear dynamics and chaos<\/span><\/strong><\/p>\n

\n

\u540e\u53f0\u56de\u590dStrogatz\u83b7\u53d6\u672c\u4e66PDF\u4e0b\u8f7d\u94fe\u63a5\u5730\u5740\u3002<\/span><\/p>\n

\n

\u672c\u4e66\u7684\u7b2c\u4e00\u7ae0\uff0cOverview\uff0c\u5bf9\u5e94\u7684\u5c31\u662f\u8fd9\u5802\u8bfe\u7684\u5185\u5bb9\u3002\u5927\u5e08\u7684Overview\u8bfe\u662f\u975e\u5e38\u6709\u4ef7\u503c\u7684\uff0c\u6bd4\u8d77\u5177\u4f53\u6280\u5de7\uff0c\u5927\u5e08\u6bd4\u6211\u4eec\u51e1\u4eba\u5f3a\u5f97\u591a\u7684\u66f4\u662f\u773c\u754c\u3002\u90a3\u5c31\u8ba9Strogatz\u6559\u6388\u5e26\u6211\u4eec\u5f00\u5f00\u773c\u754c\u5427\u3002<\/span><\/p>\n

\n

\u52a8\u529b\u5b66\u53d1\u5c55\u7684\u5386\u53f2<\/strong><\/p>\n

\n

\u5341\u4e03\u4e16\u7eaa\u4e2d\u671f\uff08mid-1600s\uff09<\/span><\/strong>\uff0c<\/span><\/strong>\u725b\u987f\u5230\u8fbe\u4ed6\u7684\u5b66\u672f\u5dc5\u5cf0\u2014\u2014\u53d1\u660e\u5fae\u79ef\u5206\u3001\u53d1\u73b0\u725b\u987f\u4e09\u5b9a\u5f8b\u548c\u4e07\u6709\u5f15\u529b\u3001\u89e3\u91ca\u884c\u661f\u56f4\u7ed5\u592a\u9633\u8fd0\u52a8\uff0c\u4e5f\u5c31\u662f\u4e8c\u4f53\u8fd0\u52a8\uff082-Body Motion\uff09\uff0c\u884c\u661f\u548c\u592a\u9633\u4e8c\u4f53\u3002<\/strong>\u4e4b\u540e\u725b\u987f\u4ef0\u6155\u8005\u4eec\u5e0c\u671b\u5c06\u4e8c\u4f53\u8fd0\u52a8\u6269\u5c55\u5230\u4e09\u4f53\u8fd0\u52a8\u65f6\uff0c\u4f46\u662f\u7531\u4e8e\u4e09\u4f53\u8fd0\u52a8\u592a\u96be\u8ba1\u7b97\uff0c\u4ed6\u4eec\u4e00\u76f4\u5361\u4f4f\u6ca1\u6709\u4ec0\u4e48\u8fdb\u5c55\u3002<\/span><\/p>\n

\n

\u4e00\u5361\u5361\u5230\u4e86\u5341\u4e5d\u4e16\u7eaa\u665a\u671f\uff08late-1800s\uff09\uff0c<\/strong>\u56e0\u4e3a\u5b9a\u91cf\u7814\u7a76\u8d70\u4e0d\u901a\uff0cPoincar\u00e9\u63d0\u51fa\u4ece\u5b9a\u6027\u89d2\u5ea6\u53bb\u7814\u7a76\u4e09\u4f53\u8fd0\u52a8\uff0c\u4f7f\u4ed6\u6210\u4e3a\u4e86\u7aa5\u89c1\u6df7\u6c8c\uff08Chaos\uff09\u7684\u7b2c\u4e00\u4eba\u3002\u4ed6\u4ece\u786e\u5b9a\u7684\u516c\u5f0f\u51fa\u53d1\uff0c\u53d1\u73b0\u4e86\u80fd\u591f\u4ea7\u751f\u4e0d\u5faa\u73af\u7684\u3001\u5bf9\u521d\u59cb\u6761\u4ef6\u654f\u611f\u7684\u884c\u4e3a\uff0c\u4ece\u800c\u8ba4\u4e3a\u65e0\u6cd5\u901a\u8fc7\u8ba1\u7b97\u957f\u671f\u7684\u7cbe\u786e\u9884\u6d4b\u4e09\u4f53\u8fd0\u52a8\u7684\u7ed3\u679c\u3002<\/span><\/p>\n

\n

\u4f46\u662f\u4ed6\u7684\u7814\u7a76\u6210\u679c\u5f53\u65f6\u5e76\u6ca1\u6709\u5f15\u8d77\u5927\u5bb6\u7684\u6ce8\u610f\uff0c\u76f4\u5230\u4e8c\u5341\u4e16\u7eaa\u4e2d\u671f\uff08mid-1900s\uff09\u4e4b\u524d\uff0c<\/strong>\u52a8\u529b\u5b66\u8fd8\u662f\u57fa\u672c\u56f4\u7ed5\u975e\u7ebf\u6027\u632f\u5b50\uff08Nonlinear Oscillator\uff09\u4ee5\u53ca\u5b83\u5728\u7269\u7406\u548c\u5de5\u7a0b\u9886\u57df\u7684\u5e94\u7528\u53d1\u5c55\u7684\uff0c\u4e3b\u8981\u5e94\u7528\u5728\u65e0\u7ebf\u7535\u3001\u96f7\u8fbe\u7b49\u65b9\u9762\u3002<\/span><\/p>\n

\n

\u5230\u4e861950s\uff0c<\/span><\/strong>\u8ba1\u7b97\u673a\u5f00\u59cb\u51fa\u73b0\uff0c\u4eba\u4eec\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u6765\u6a21\u62df\u52a8\u529b\u5b66\u7cfb\u7edf\u8fdb\u884c\u5b9e\u9a8c\u3002<\/span><\/p>\n

\n

1963\u5e74\uff0c<\/span><\/strong>Lorenz\u5728\u4f7f\u7528\u8ba1\u7b97\u673a\u6765\u6a21\u62df\u5927\u6c14\u7cfb\u7edf\uff0c\u7814\u7a76\u5929\u6c14\u9884\u6d4b\u7684\u65f6\u5019\uff0c\u53d1\u73b0\u7b80\u5355\u7684\u51e0\u4e2a\u56e0\u7d20\u590d\u5408\u5c31\u4ea7\u751f\u4e86\u4e00\u79cd\u795e\u5947\u7684\u73b0\u8c61\uff0c\u8fd9\u4e2a\u52a8\u529b\u7cfb\u7edf\u4e0d\u4f1a\u7a33\u5b9a\u4e0b\u6765\u53d8\u6210\u5468\u671f\u6027\u6216\u8005\u9759\u6b62\u7684\u70b9\uff0c\u800c\u662f\u4e00\u76f4\u4ee5\u4e00\u79cd\u975e\u5468\u671f\u6027\u7684\u4e0d\u89c4\u5219\u7684\u65b9\u5f0f\u9707\u8361\uff0c\u8774\u8776\u5f62\u72b6\u7684Chaos\u56fe\u5f62\u5c31\u662f\u5728\u4ed6\u7684\u5b9e\u9a8c\u4e2d\u5f97\u5230\u7684\u3002<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u6df7\u6c8c\u548c\u975e\u7ebf\u6027<\/span><\/strong><\/p>\n

\n

1970\u5e74\u540e\uff0c<\/span><\/strong>\u6df7\u6c8c\u7406\u8bba\u6709\u4e86\u957f\u8db3\u7684\u53d1\u5c55\uff0cRuelle\u548cTakens\u7814\u7a76\u4e86\u6270\u6d41\uff08Turbulence\uff09\u7684\u89e6\u53d1\uff1bMay\u5219\u5728\u751f\u7269\u5b66\u9886\u57df\u63d0\u51fa\u7528\u6df7\u6c8c\u6765\u89e3\u91ca\u4eba\u53e3\u589e\u957f\u6a21\u578b\uff0c\u8ba9\u5927\u5bb6\u7406\u89e3\u5230\u4e86\u975e\u7ebf\u6027\u7684\u91cd\u8981\u6027\u548c\u7528\u7ebf\u6027\u6765\u7b80\u5316\u4ea7\u751f\u7684\u95ee\u9898\uff1b\u7269\u7406\u5b66\u5bb6Feigenbaum\u5219\u53d1\u73b0\u4e86\u5728\u4e0d\u540c\u9886\u57df\u3001\u4e0d\u540c\u7279\u5f81\u7684\u7cfb\u7edf\uff0c\u5f80\u5f80\u53d1\u5c55\u51fa\u76f8\u4f3c\u7684\u6df7\u6c8c\u7cfb\u7edf\uff0c\u63d0\u51fa\u8fd9\u662f\u4e00\u4e2a\u666e\u9002\u7684\u5b9a\u5f8b\uff08Universal Law\uff09\u3002<\/span><\/p>\n

\n

\u540c\u6837\u57281970s\uff0c<\/span><\/strong>Mandelbrot\u53d1\u73b0\u4e86\u5206\u5f62\uff08Fractal\uff09\uff0c\u76f4\u5230\u73b0\u5728\u7231\u597d\u8005\u4eec\u8fd8\u5728\u7528\u8ba1\u7b97\u673a\u753b\u51fa\u6f02\u4eae\u7684\u65e0\u9650Zoom in\u7684Mandelbrot\u5206\u5f62\u3002<\/span><\/p>\n

\n

1980\u5e74\u540e\uff0c<\/span><\/strong>\u6df7\u6c8c\u7406\u8bba\u5f00\u59cb\u6210\u4e3a\u70ed\u95e8\u7814\u7a76\u3002<\/span><\/p>\n

\n

\u4e66\u4e2d\u7ed9\u51fa\u8868\u683c\uff1a<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

A Capsule History of Dynamics<\/span><\/strong><\/p>\n

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\n

\u52a8\u529b\u5b66\u7684\u6570\u5b66\u903b\u8f91\u7ed3\u6784<\/strong><\/p>\n

\n

\u5c0f\u5fc3\uff0c\u8fd9\u91cc\u8981\u51fa\u73b0\u6570\u5b66\u516c\u5f0f\u4e86\u3002<\/span><\/p>\n

\n

\u4e3a\u4e86\u628a\u73b0\u5b9e\u4e16\u754c\u7684\u8fd0\u52a8\u5f52\u7c7b\uff0cStrogatz\u6559\u6388\u63d0\u51fa\u53ef\u4ee5\u6839\u636e\u4e24\u4e2a\u6307\u6807\uff1a\u4e00\u4e2a\u662f\u52a8\u529b\u5b66\u7cfb\u7edf\u7ef4\u6570\uff0c\u4e5f\u53ef\u4ee5\u79f0\u4e3a\u9636\u6570\uff0c\u5c31\u662f\u7cfb\u7edf\u6d89\u53ca\u53d8\u91cf\u4e2a\u6570\uff0c\u53e6\u4e00\u4e2a\u662f\u8fd9\u4e2a\u8fd0\u52a8\u662f\u7ebf\u6027\u7684\u8fd8\u662f\u975e\u7ebf\u6027\u7684\u3002<\/strong><\/span><\/p>\n

\n

\u90a3\u6211\u4eec\u5148\u6765\u770b\u770b\u4ed6\u662f\u600e\u4e48\u7528\u6570\u5b66\u6765\u63cf\u8ff0\u7cfb\u7edf\u3002<\/span><\/p>\n

\n

\u4f8b1\uff1a\u725b\u987f\u7269\u7406\u4e2d\u7684\u4e00\u4e2a\u5300\u901f\u8fd0\u52a8\u7684\u7269\u4f53\u3002<\/span><\/strong><\/p>\n

\n

\u6839\u636e\u521d\u4e2d\u5b66\u8fc7\u7684\u77e5\u8bc6\uff0c\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a\u7269\u4f53\u7684\u901f\u5ea6v\u662f\u6052\u5b9a\u7684\uff0c\u4e0d\u7ba1\u7269\u4f53\u8fd0\u52a8\u5230\u54ea\u91cc\u3002\u6211\u4eec\u53ef\u4ee5\u753b\u56fe\uff0c\u7eb5\u5750\u6807\u662f\u901f\u5ea6v\uff0c\u6a2a\u5750\u6807\u662f\u7269\u4f53\u7684\u4f4d\u7f6e\u3002<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u4f8b1<\/span><\/strong><\/p>\n

\n

\u8fd9\u91cc\u7684\u901f\u5ea6v\uff0c\u5b9e\u9645\u5c31\u662fdx\/dt\uff0c\u5c31\u662f\u8fd9\u4e2a\u7269\u4f53\u7684\u4f4d\u7f6e\u7684\u53d8\u5316\u7387\uff0c\u6309\u7167\u725b\u987f\u5bf9\u5bfc\u6570\u7684\u8bb0\u53f7\u65b9\u6cd5\uff0c\u7528x\u4e0a\u9762\u52a0\u4e00\u70b9\u8868\u793a\u3002<\/span><\/p>\n

\n

\u8fd9\u6837\u8fd9\u4e2a\u7cfb\u7edf\u7684\u6570\u5b66\u516c\u5f0f\u5c31\u662f\uff1a<\/span>\"\u96c6\u667a\"\uff0c\u5176\u4e2da\u662f\u4e00\u4e2a\u5e38\u6570\u3002<\/span><\/p>\n

\n

\u8fd9\u4e2a\u516c\u5f0f\u91cc\uff0c\u6709\u4e00\u4e2a\u53d8\u91cf\uff0c<\/span>\"\u96c6\u667a\"\uff0cStrogatz\u6559\u6388\u79f0\u8fd9\u662f\u4e00\u7ef4\u7684\uff1b\u7136\u540e\u7b49\u5f0f\u53f3\u8fb9\u4e0d\u5305\u542b\u4efb\u4f55\u5e73\u65b9\u3001\u53d8\u91cf\u76f8\u4e58\u3001\u6216\u8005\u4ee5\u53d8\u91cf\u4e3a\u8f93\u5165\u7684\u51fd\u6570\uff0c\u4ed6\u79f0\u8fd9\u662f\u7ebf\u6027\u7684\u3002\u4e5f\u5c31\u662f\u8fd9\u662f\u4e00\u4e2a\u4e00\u7ef4\u7ebf\u6027\u7cfb\u7edf\u3002<\/span><\/p>\n

\n

\u4f8b2\uff1a\u725b\u987f\u7269\u7406\u4e2d\u7684\u4e00\u4e2a\u53d7\u4f5c\u7528\u529b\u52a0\u901f\u8fd0\u52a8\u7684\u7269\u4f53\u3002<\/span><\/strong><\/p>\n

\n

\u7eb5\u5750\u6807\u662f\u7269\u4f53\u7684\u901f\u5ea6v\uff0c\u6a2a\u5750\u6807\u662f\u7269\u4f53\u7684\u4f4d\u7f6ex\uff0c\u6211\u4eec\u53ef\u4ee5\u753b\u56fe\uff1a<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u4f8b2<\/span><\/strong><\/p>\n

\n

\u6309\u7167\u4e0a\u9762\u7684\u7ea6\u5b9a\uff0c\u6211\u4eec\u53ef\u4ee5\u5199\u51fa\u8fd9\u4e2a\u7cfb\u7edf\u7684\u6570\u5b66\u516c\u5f0f\uff1a<\/span>\"\u96c6\u667a\"\uff0c\u5176\u4e2da\u3001b\u662f\u5e38\u6570\u3002\u6240\u4ee5\u8fd9\u4e2a\u7cfb\u7edf\u4e5f\u662f\u4e00\u7ef4\u7ebf\u6027\u7cfb\u7edf\u3002<\/span><\/p>\n

\n

\u4f8b3\uff1aDamped oscillator\u3002\u4e00\u4e2a\u7269\u4f53\u4ee5\u4e00\u5b9a\u7684\u521d\u901f\u5ea6\uff0c\u5728\u6709\u963b\u529b\u7684\u60c5\u51b5\u4e0b\u968f\u5f39\u7c27\u632f\u52a8\u6162\u6162\u505c\u6ede\u7684\u8fd0\u52a8\u3002<\/span><\/strong><\/p>\n

\n

\u7eb5\u5750\u6807\u662f\u7269\u4f53\u7684\u901f\u5ea6v\uff0c\u6a2a\u5750\u6807\u662f\u65f6\u95f4t\uff0c\u6211\u4eec\u53ef\u4ee5\u753b\u56fe\uff1a<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u4f8b3-1<\/span><\/strong><\/p>\n

\u6765\u6e90\uff1ahttp:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/oscda.html#c1<\/strong><\/p>\n

\n

Damped oscillator\u7684\u8fd0\u52a8\u516c\u5f0f\uff1a<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u4f8b3-2<\/span><\/strong><\/p>\n

\n

\u5047\u8bbe<\/span>\"\u96c6\u667a\",<\/span>\"\u96c6\u667a\"<\/p>\n

\n

\u90a3\u4e48<\/span>\"\u96c6\u667a\"\uff0c<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\n

\u4e0a\u9762\u4e24\u6761\"\u96c6\u667a\"\u548c<\/span>\"\u96c6\u667a\"\u7684\u516c\u5f0f\uff0c\u5c31\u662f\u63cf\u8ff0\u8fd9\u4e2a\u7cfb\u7edf\u7684\u6570\u5b66\u516c\u5f0f\u3002\u901a\u8fc7\u8fd9\u7ec4\u516c\u5f0f\u53ef\u4ee5\u770b\u51fa\uff0c\u8fd9\u4e2a\u7cfb\u7edf\u662f\u4e8c\u7ef4\u7684\u7ebf\u6027\u7684\u7cfb\u7edf\u3002<\/span><\/p>\n

\n

\u4f8b4\uff1aPendulum\u3002\u4e00\u4e2a\u7269\u4f53\u5728\u6446\u52a8\u3002<\/span><\/strong><\/p>\n

\"\u96c6\u667a\"\uff0c\u4e5f\u53ef\u4ee5\u5199\u6210 <\/span>\"\u96c6\u667a\"\uff0c<\/span><\/p>\n

\u5047\u8bbe<\/span>\"\u96c6\u667a\"\uff0c\u90a3\u4e48<\/span><\/p>\n

\"\u96c6\u667a\"<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u901a\u8fc7\u8fd9\u7ec4\u516c\u5f0f\u53ef\u4ee5\u770b\u51fa\uff0c\u8fd9\u4e2a\u7cfb\u7edf\u662f\u4e8c\u7ef4\u7684\uff0c\u540c\u65f6\u56e0\u4e3a\u53f3\u4fa7\u6709\u53d8\u91cfx1\u8f93\u5165sin\u51fd\u6570\uff0c\u6240\u4ee5\u8fd9\u4e2a\u7cfb\u7edf\u662f\u975e\u7ebf\u6027\u7684\u3002\u8fd9\u662f\u4e00\u4e2a\u4e8c\u7ef4\u975e\u7ebf\u6027\u7cfb\u7edf\u3002<\/span><\/p>\n

\n

\n

\u7528\u52a8\u529b\u5b66\u7684\u89c6\u89d2\u770b\u4e16\u754c<\/strong><\/p>\n

\n

\u7ed9\u51fa\u4e86\u7cfb\u7edf\u7684\u7ef4\u5ea6\uff08\u6216\u8005\u8bf4\u9636\u6570\uff09\u7684\u5b9a\u4e49\uff0c\u518d\u7ed9\u51fa\u4e86\u7ebf\u6027\u975e\u7ebf\u6027\u7684\u5b9a\u4e49\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u628a\u8fd9\u4e2a\u4e16\u754c\u7684\u8fd0\u52a8\u8fdb\u884c\u5206\u7c7b\u4e86\u3002Strogatz\u6559\u6388\u7ed9\u51fa\u4e86\u4e00\u5f20\u5927\u56fe\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

A Dynamical View of the World<\/span><\/strong><\/p>\n

\n

\u8fd9\u56fe\u5728\u4e0a\u8bfe\u65f6\u5019\u5199\u5728\u9ed1\u677f\u4e0a\u662f\u8fd9\u6837\u7684\uff1a<\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n

\u9ed1\u677f\u4e0a\u7684A Dynamical View of the World<\/span><\/strong><\/p>\n

\n

\u8fd9\u5c31\u662fStrogatz\u6559\u6388\u5bf9\u4e16\u754c\u4e0a\u7684\u8fd0\u52a8\u7684\u5f52\u7c7b<\/strong>\u7684\u7406\u89e3\u3002<\/span><\/p>\n

\n

\u7b2c\u4e00\u884c\u662f\u7ebf\u6027\u7cfb\u7edf\uff0c<\/strong>\u6211\u4eec\u5c31\u5148\u4e0d\u5173\u5fc3\u4e86\uff0c\u7b2c\u4e8c\u884c\u662f\u975e\u7ebf\u6027\u7cfb\u7edf\uff0c<\/strong>\u4ece\u4e00\u7ef4\uff08n=1\uff09\u5230\u4e8c\u7ef4\u5230\u4e09\u7ef4\uff0c\u8fd9\u4e09\u90e8\u5206\u5c31\u662f\u8fd9\u672c\u4e66\u4e3b\u8981\u6559\u6388\u7684\u5185\u5bb9\u3002<\/span><\/p>\n

\n

\u800c\u8fd9\u5f20\u56fe\u7684\u53f3\u4e0b\u89d2\uff0c\u5f53n\u5f88\u5927\uff08n>>1\uff09\u7684\u65f6\u5019\uff0c\u5c31\u662fNetwork Science\u7814\u7a76\u7684\u9886\u57df\uff0c\u5982\u679cn\u662f\u8fde\u7eed\u7684\u8bdd\uff0c\u8fd9\u65f6\u5c31\u662f\u5e7f\u4e49\u76f8\u5bf9\u8bba\u3001\u6270\u6d41\u7b49\u7814\u7a76\u7684\u9886\u57df\uff0c\u6574\u4e2a\u53f3\u4e0b\u89d2\uff0c\u7edf\u79f0\u4e3aComplex Systems\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u7406\u89e3\u4e86Chaos\u7684\u6570\u5b66\u8868\u8fbe\u4e4b\u540e\uff0c\u518d\u5c06\u53d8\u91cf\u4ece3\u6269\u5c55\u5230\u51e0\u4e07\u51e0\u4ebf\u4e2a\uff0c\u5c31\u53ef\u4ee5\u79f0\u4e4b\u4e3aNetwork Science\u4e86\u3002<\/span><\/p>\n

\n

\u4f5c\u8005\uff1a\u5218\u601d\u8fbe<\/p>\n

\u7f16\u8f91\uff1a\u5b5f\u5a55<\/p>\n<\/blockquote>\n

\u63a8\u8350\u9605\u8bfb<\/strong><\/p>\n

\u6570\u5b57\u65f6\u4ee3\u7684\u793e\u4f1a\u751f\u6001\u5b66\uff1a\u89e3\u51b3\u5168\u7403\u5316\u4e16\u754c\u4e2d\u7684\u590d\u6742\u95ee\u9898 | \u4e66\u7c4d\u63a8\u8350<\/span><\/strong><\/a><\/p>\n

\u89e3\u5bc6\u590d\u6742\u7cfb\u7edf\uff1a\u79d1\u5b66\u5927\u6311\u6218 | \u65b0\u4e66\u63a8\u8350<\/span><\/strong><\/a><\/p>\n

\u8bba\u6587\u901f\u9012\uff1a\u4f5c\u4e3a\u590d\u6742\u7f51\u7edc\u7684\u6df1\u5ea6\u5b66\u4e60\u7cfb\u7edf<\/span><\/strong><\/a><\/p>\n

\u6df7\u6c8c\u3001\u5206\u5f62\u7406\u8bba\u53ca\u5176\u5728\u4fe1\u606f\u79d1\u5b66\u4e2d\u7684\u5e94\u7528 | IWCFTA2018<\/span><\/strong><\/a><\/p>\n

\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/span><\/strong><\/span><\/a><\/p>\n

\"\u96c6\u667a\"<\/div>\n
\u96c6\u667aAI\u5b66\u56ed\uff1a<\/p>\n

https:\/\/campus.swarma.org<\/p>\n

\n
\n
\"\u96c6\u667a\"<\/div>\n
\n
\n
\n
\n
\n
\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

\n

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

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

 <\/p>\n

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

\"\u96c6\u667a\"<\/p>\n<\/section>\n

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

\u539f\u6587\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff08 \u96c6\u667a\u4ff1\u4e50\u90e8 \uff09\uff1a\u96c6\u667a<\/a><\/p><\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5982\u679c\u4f60\u548c\u6211\u4e00\u6837\uff0c\u5bf9\u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff08Nonlinear Dynamics\uff09\u3001\u6df7\u6c8c\uff08Chaos\uff09\u3001\u5206\u5f62\uff08Fractals\uff09\u3001\u7f51\u7edc\u79d1\u5b66\uff08Network Science\uff09\u3001\u590d\u6742\u7cfb\u7edf\uff08Complex Systems\uff09\u611f\u5174\u8da3\uff0c\u4f46\u662f\u6709\u65f6\u5019\u5374\u89c9\u5f97\u4ed6\u4eec\u90fd\u5dee\u4e0d\u591a\u662f\u4e00\u56de\u4e8b\uff0c\u641e\u4e0d\u6e05\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u90a3\u4e48\u8fd9\u5802Strogatz\u6559\u6388\u7684\u8bfe…<\/p>\n","protected":false},"author":1,"featured_media":14156,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[18],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/12060"}],"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=12060"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/12060\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/14156"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12060"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12060"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12060"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=12060"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}