{"id":22581,"date":"2020-12-10T18:08:00","date_gmt":"2020-12-10T10:08:00","guid":{"rendered":"https:\/\/swarma.org\/?p=22581"},"modified":"2020-12-10T18:08:00","modified_gmt":"2020-12-10T10:08:00","slug":"%e4%bb%80%e4%b9%88%e6%98%af%e5%8a%a8%e5%8a%9b%e7%b3%bb%e7%bb%9f%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=22581","title":{"rendered":"\u4ec0\u4e48\u662f\u52a8\u529b\u7cfb\u7edf\u7406\u8bba | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u548c\u6df7\u6c8c\u7406\u8bba chaos Theory \u90fd\u5bf9\u52a8\u529b\u7cfb\u7edf\u7684\u957f\u671f\u884c\u4e3a\u8fdb\u884c\u5b9a\u6027\u7814\u7a76\u3002\u8fd9\u91cc\u8bf4\u7684\u5b9a\u6027\u7814\u7a76\uff0c\u662f\u6307\u4fa7\u91cd\u4e8e\u7814\u7a76\u52a8\u529b\u7cfb\u7edf\u7684\u6027\u8d28\uff0c\u53bb\u56de\u7b54\u8bf8\u5982\u201c\u7cfb\u7edf\u957f\u671f\u6765\u770b\uff0c\u4f1a\u8fbe\u5230\u6216\u8d8b\u4e8e\u7a33\u6001\u5417\uff1f\u201d\u3001\u201c\u5982\u679c\u53ef\u4ee5\uff0c\u90fd\u6709\u54ea\u4e9b\u53ef\u80fd\u8fbe\u5230\u6216\u8d8b\u8fd1\u7684\u7a33\u6001\uff1f\u201d\u3001\u201d\u7cfb\u7edf\u7684\u957f\u671f\u884c\u4e3a\u53d7\u521d\u59cb\u6761\u4ef6\u5f71\u54cd\u5417\uff1f\u201c\u4e4b\u7c7b\u7684\u95ee\u9898\uff0c\u800c\u4e0d\u90a3\u4e48\u5173\u6ce8\u4e8e\uff08\u7ecf\u5e38\u4e5f\u4e0d\u53ef\u80fd\uff09\u6c42\u52a8\u529b\u7cfb\u7edf\u65b9\u7a0b\u7684\u7cbe\u786e\u89e3\u3002<\/span><\/p>\n


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\u5728\u80fd\u8fdb\u884c\u9ad8\u901f\u8ba1\u7b97\u7684\u673a\u5668\u51fa\u73b0\u4e4b\u524d\uff0c\u4eba\u4eec\u9700\u8981\u901a\u8fc7\u590d\u6742\u5de7\u5999\u7684\u6570\u5b66\u6280\u5de7\u624d\u80fd\u6c42\u89e3\u5b9a\u4e49\u52a8\u529b\u7cfb\u7edf\u7684\u65b9\u7a0b\uff0c\u8fd9\u6837\u8fd8\u53ea\u80fd\u6c42\u89e3\u4e00\u5c0f\u7c7b\u52a8\u529b\u7cfb\u7edf\u95ee\u9898\u3002\u968f\u7740\u7535\u5b50\u8ba1\u7b97\u673a\u7684\u8bde\u751f\u548c\u8ba1\u7b97\u8d44\u6e90\u7684\u4e0d\u65ad\u63d0\u5347\uff0c\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u4e2d\u7684\u6570\u5b66\u6280\u5de7\u4e5f\u9010\u6e10\u548c\u79d1\u5b66\u8ba1\u7b97\u65b9\u6cd5\u76f8\u7ed3\u5408\uff0c\u540c\u65f6\u7ee7\u7eed\u7740\u773c\u4e8e\u5b9a\u6027\u7814\u7a76\u3002<\/span><\/p>\n


<\/p>\n

\u4e00\u4e9b\u4f18\u79c0\u7684\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u4e13\u8457\u5305\u62ec\uff1aLuenberger (1979), Padulo & Arbib (1974), and Strogatz (1994).<\/span><\/p>\n


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

    \n
  • \n

    Luenberger, David G. (1979). Introduction to dynamic systems: theory, models, and applications. Wiley. ISBN 978-0-471-02594-8. OCLC 4195122.<\/span><\/p>\n<\/li>\n

  • \n

    Padulo, Louis; Arbib, Michael A. (1974). System theory: a unified state-space approach to continuous and discrete systems. Saunders. ISBN 9780721670355. OCLC 947600.<\/span><\/p>\n<\/li>\n

  • \n

    Strogatz, Steven H. (1994). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Addison Wesley. ISBN 978-0-7382-0453-6. OCLC 49839504.<\/span><\/p>\n<\/li>\n<\/ul>\n


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    \u52a8\u529b\u7cfb\u7edf<\/span><\/strong><\/section>\n
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    \u52a8\u529b\u7cfb\u7edf\u5728\u67d0\u4e2a\u65f6\u523b\u7684\u7cfb\u7edf\u72b6\u6001\uff0c\u7531\u4e00\u7ec4\u5b9e\u6570\u6240\u8868\u793a\u548c\u786e\u5b9a\uff0c\u6216\u8005\u66f4\u4e00\u822c\u7684\u8bf4\uff0c\u7531\u9002\u5f53\u7684\u72b6\u6001\u7a7a\u95f4\u4e2d\u7684\u4e00\u7ec4\u70b9\u7684\u96c6\u5408\u6765\u8868\u793a\u548c\u786e\u5b9a\u3002\u7cfb\u7edf\u72b6\u6001\u7684\u5fae\u5c0f\u53d8\u5316\u5bf9\u5e94\u4e8e\u6570\u503c\u7684\u5fae\u5c0f\u53d8\u5316\u3002\u8fd9\u4e9b\u6570\u5b57\u4e5f\u662f\u67d0\u79cd\u51e0\u4f55\u7a7a\u95f4\u2014\u2014\u67d0\u79cd\u6d41\u5f62 manifold\u2014\u2014\u7684\u5750\u6807\u503c\u3002\u52a8\u529b\u7cfb\u7edf\u7684\u6f14\u5316\u5f8b\u662f\u4e00\u79cd\u56fa\u5b9a\u7684\u89c4\u5219\uff0c\u5b83\u63cf\u8ff0\u4e86\u7cfb\u7edf\u4ece\u5f53\u524d\u7684\u72b6\u6001\u5982\u4f55\u6f14\u5316\u4e3a\u672a\u6765\u7684\u72b6\u6001\u3002\u8fd9\u4e2a\u89c4\u5219\u53ef\u80fd\u662f\u786e\u5b9a\u6027\u7684\uff08\u53ef\u4ee5\u7531\u7ed9\u5b9a\u7684\u7cfb\u7edf\u5f53\u524d\u72b6\u6001\uff0c\u7cbe\u786e\u5730\u9884\u6d4b\uff0c\u7cfb\u7edf\u7ecf\u8fc7\u67d0\u7ed9\u5b9a\u65f6\u95f4\u6bb5\u540e\uff0c\u90a3\u4e00\u77ac\u95f4\u7684\u7cfb\u7edf\u72b6\u6001\uff09\uff0c\u4e5f\u53ef\u80fd\u662f\u968f\u673a\u6027\u7684\uff08\u7cfb\u7edf\u72b6\u6001\u7684\u6f14\u5316\u53ea\u80fd\u7528\u786e\u5207\u77e5\u6653\u7684\u6982\u7387\u8fdb\u884c\u9884\u6d4b\uff09\u3002<\/span><\/section>\n

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    \u52a8\u529b\u4e3b\u4e49<\/span><\/strong><\/span><\/section>\n
    \u52a8\u529b\u4e3b\u4e49 dynamicism\uff0c\u4e5f\u79f0\u52a8\u6001\u5047\u8bbe dynamic hypothesis \uff0c\u6216\u79f0\u8ba4\u77e5\u79d1\u5b66\u7684\u52a8\u6001\u5047\u8bbe dynamic hypothesis in cognitive science \u6216\u52a8\u6001\u8ba4\u77e5 dynamic cognition\uff0c\u662f\u4e00\u79cd\u8ba4\u77e5\u79d1\u5b66\u9886\u57df\u7684\u65b0\u65b9\u6cd5\uff0c\u4ee5\u54f2\u5b66\u5bb6Tim van Gelder\u7684\u5de5\u4f5c\u4e3a\u5178\u578b\u3002\u8fd9\u79cd\u65b9\u6cd5\u63d0\u51fa\uff0c\u76f8\u6bd4\u4e8e\u4f20\u7edf\u7684\u8ba1\u7b97\u673a\u6a21\u578b\uff0c\u5fae\u5206\u65b9\u7a0b\u66f4\u9002\u5408\u4e8e\u5bf9\u8ba4\u77e5\u8fdb\u884c\u5efa\u6a21\u3002<\/span><\/section>\n

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    \u6570\u5b66\u4e0a\u6765\u8bb2\uff0c\u975e\u7ebf\u6027\u7cfb\u7edf nonlinear system\u662f\u6307\u7cfb\u7edf\u4e0d\u662f\u7ebf\u6027\u7684\uff0c\u5373\u8fd9\u4e00\u7cfb\u7edf\u4e0d\u6ee1\u8db3\u53e0\u52a0\u539f\u7406\u3002\u66f4\u901a\u4fd7\u5730\u8bf4\uff0c\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7cfb\u7edf\u72b6\u6001\u91cf\uff08\u5728\u5b9a\u4e49\u7cfb\u7edf\u7684\u5fae\u5206\/\u5dee\u5206\u65b9\u7a0b\u4e2d\uff0c\u6240\u8981\u6c42\u89e3\u7684\u56e0\u53d8\u91cf\uff09\u4e0d\u80fd\u88ab\u5199\u6210\u67d0\u4e9b\u72ec\u7acb\u5206\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/span><\/section>\n


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    \u7531\u4e8e\u8fd9\u4e9b\u51fd\u6570\u7684”\u6b21\u6570” degree \u662f0\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4\u8fd9\u6837\u7684\u7cfb\u7edf\u662f\u975e\u9f50\u6b21\u7684\uff0c\u8fd9\u4e9b\u51fd\u6570\u6240\u6784\u6210\u7684\u9879\u88ab\u79f0\u4e3a\u975e\u9f50\u6b21\u9879\u3002\u6839\u636e\u7ebf\u6027\u7cfb\u7edf\u7684\u4e25\u683c\u5b9a\u4e49\uff0c\u5373\u9700\u8981\u6ee1\u8db3\u53e0\u52a0\u5b9a\u7406\uff0c\u975e\u9f50\u6b21\u7ebf\u6027\u7cfb\u7edf\u5b9e\u9645\u4e0a\u4e0d\u80fd\u7b97\u4f5c\u7ebf\u6027\u7cfb\u7edf\uff0c\u800c\u662f\u4eff\u5c04\u7cfb\u7edf affine system\u3002\uff08\u8fd9\u91cc\u53ef\u4ee5\u5bf9\u6bd4\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u548c\u975e\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u533a\u522b\uff09\u3002<\/span><\/p>\n


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    \u7b97\u672f\u52a8\u529b\u5b66<\/span><\/strong><\/p>\n

    \u7b97\u672f\u52a8\u529b\u5b66 Arithmetic Dynamics\u662f20\u4e16\u7eaa90\u5e74\u4ee3\u51fa\u73b0\u7684\u4e00\u4e2a\u9886\u57df\uff0c\u878d\u5408\u4e86\u52a8\u529b\u7cfb\u7edf\u548c\u6570\u8bba\u8fd9\u4e24\u4e2a\u6570\u5b66\u9886\u57df\u3002\u7ecf\u5178\u7684\u79bb\u6563\u52a8\u529b\u5b66\u7814\u7a76\u7684\u662f\u590d\u5e73\u9762\u6216\u5b9e\u5b9e\u6570\u8f74\u7684\u81ea\u6620\u5c04\u7684\u8fed\u4ee3\uff0c\u7b97\u672f\u52a8\u529b\u5b66\u662f\u5728\u53cd\u590d\u5e94\u7528\u591a\u9879\u5f0f\u6216\u6709\u7406\u51fd\u6570\u7684\u60c5\u51b5\u4e0b\u5bf9\u6574\u6570\uff0c\u6709\u7406\u6570\uff0cp\u8fdb\u6570(p-adic)\u548c\/\u6216\u4ee3\u6570\u70b9\u7684\u6570\u8bba\u6027\u8d28\u8fdb\u884c\u7814\u7a76\u3002<\/span><\/p>\n


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    \u6df7\u6c8c\u7406\u8bba<\/span><\/strong><\/p>\n

    \u6df7\u6c8c\u7406\u8bba Chaos theory \u63cf\u8ff0\u4e86\u67d0\u4e9b\u72b6\u6001\u968f\u65f6\u95f4\u6f14\u5316\u7684\u52a8\u529b\u7cfb\u7edf\u7684\u884c\u4e3a\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u53ef\u80fd\u8868\u73b0\u51fa\u5bf9\u521d\u59cb\u6761\u4ef6\u9ad8\u5ea6\u654f\u611f\u7684\u7279\u70b9\uff08\u901a\u5e38\u88ab\u79f0\u4e3a\u8774\u8776\u6548\u5e94 Butterfly Effect\uff09\u3002\u7531\u4e8e\u8fd9\u79cd\u654f\u611f\u6027\uff0c\u5728\u521d\u59cb\u6761\u4ef6\u4e0b\u8868\u73b0\u4e3a\u6270\u52a8\u5448\u6307\u6570\u589e\u957f\uff0c\u56e0\u6b64\u6df7\u6c8c\u7cfb\u7edf\u7684\u884c\u4e3a\u4f3c\u4e4e\u662f\u968f\u673a\u7684\u3002\u5373\u4f7f\u8fd9\u4e9b\u7cfb\u7edf\u662f\u786e\u5b9a\u6027\u7684\uff0c\u4e5f\u4f1a\u53d1\u751f\u8fd9\u79cd\u60c5\u51b5\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u4eec\u7684\u672a\u6765\u52a8\u529b\u5b8c\u5168\u7531\u5176\u521d\u59cb\u6761\u4ef6\u5b9a\u4e49\uff0c\u800c\u6ca1\u6709\u6d89\u53ca\u968f\u673a\u5143\u7d20\u3002\u8fd9\u79cd\u884c\u4e3a\u79f0\u4e3a\u786e\u5b9a\u6027\u6df7\u4e71\uff0c\u6216\u7b80\u79f0\u4e3a\u6df7\u4e71\u3002<\/span><\/p>\n


    <\/p>\n

    \u590d\u6742\u7cfb\u7edf<\/span><\/strong><\/p>\n

    \u590d\u6742\u7cfb\u7edf Complex Systems \u662f\u7814\u7a76\u81ea\u7136\u3001\u793e\u4f1a\u548c\u79d1\u5b66\u4e2d\u590d\u6742\u73b0\u8c61\u7684\u5171\u540c\u6027\u8d28\u7684\u79d1\u5b66\u9886\u57df\u3002\u5b83\u4e5f\u88ab\u79f0\u4e3a\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u3001\u590d\u6742\u6027\u79d1\u5b66\u3001\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u548c\u5173\u4e8e\u590d\u6742\u6027\u7684\u79d1\u5b66\u3002\u8fd9\u4e9b\u7cfb\u7edf\u7684\u5173\u952e\u95ee\u9898\u5728\u4e8e\u5bf9\u7cfb\u7edf\u7684\u5f62\u5f0f\u5316\u5efa\u6a21\u4e0e\u4eff\u771f\u7684\u56f0\u96be\u3002\u56e0\u6b64\uff0c\u590d\u6742\u7cfb\u7edf\u662f\u6839\u636e\u5728\u4e0d\u540c\u7684\u7814\u7a76\u8bed\u5883\u4e2d\u7684\u4e0d\u540c\u5c5e\u6027\u6765\u5b9a\u4e49\u7684\u3002<\/span><\/p>\n


    <\/p>\n

    \u590d\u6742\u7cfb\u7edf\u7684\u7814\u7a76\u4e3a\u8bb8\u591a\u79d1\u5b66\u9886\u57df\u5e26\u6765\u4e86\u65b0\u7684\u6d3b\u529b\uff0c\u5728\u8fd9\u4e9b\u9886\u57df\u4e2d\uff0c\u66f4\u4e3a\u5178\u578b\u7684\u7b80\u5316\u4e3b\u4e49\u7b56\u7565\u5df2\u7ecf\u4e0d\u8db3\u4ee5\u63d0\u4f9b\u7814\u7a76\u52a8\u529b\u3002\u590d\u6742\u7cfb\u7edf\u901a\u5e38\u88ab\u7528\u4f5c\u4e00\u4e2a\u5e94\u7528\u5e7f\u6cdb\u7684\u7814\u7a76\u65b9\u6cd5\u672f\u8bed\uff0c\u5e76\u6db5\u76d6\u8bb8\u591a\u4e0d\u540c\u7684\u5b66\u79d1\uff0c\u5305\u62ec\u795e\u7ecf\u79d1\u5b66\u3001\u793e\u4f1a\u79d1\u5b66\u3001\u6c14\u8c61\u5b66\u3001\u5316\u5b66\u3001\u7269\u7406\u5b66\u3001\u8ba1\u7b97\u673a\u79d1\u5b66\u3001\u5fc3\u7406\u5b66\u3001\u4eba\u5de5\u751f\u547d\u3001\u8fdb\u5316\u8ba1\u7b97\u3001\u7ecf\u6d4e\u5b66\u3001\u5730\u9707\u9884\u6d4b\u3001\u5206\u5b50\u751f\u7269\u5b66\u4ee5\u53ca\u5bf9\u6d3b\u7ec6\u80de\u7684\u7814\u7a76\u7b49\u8bb8\u591a\u4e0d\u540c\u5b66\u79d1\u7684\u95ee\u9898\u7684\u7814\u7a76\u65b9\u6cd5\u3002<\/span><\/p>\n


    <\/p>\n

    \u63a7\u5236\u7406\u8bba<\/span><\/strong><\/p>\n

    \u63a7\u5236\u7406\u8bba Control Theory \u662f\u5de5\u7a0b\u548c\u6570\u5b66\u7684\u4e00\u4e2a\u4ea4\u53c9\u5b66\u79d1\u3002\u63a7\u5236\u7406\u8bba\u662f\u4e00\u4e2a\u7814\u7a76\u5982\u4f55\u8c03\u6574\u52a8\u529b\u7cfb\u7edf\u7279\u6027\u7684\u7406\u8bba\uff0c\u5b83\u4e5f\u662f\u5de5\u7a0b\u548c\u6570\u5b66\u7684\u4e00\u4e2a\u4ea4\u53c9\u5b66\u79d1\uff0c\u9010\u6e10\u7684\u5e94\u7528\u5728\u8bb8\u591a\u793e\u4f1a\u79d1\u5b66\u4e2d\uff0c\u4f8b\u5982\u5fc3\u7406\u5b66\u3001\u793e\u4f1a\u5b66\uff08\u793e\u4f1a\u5b66\u4e2d\u7684\u63a7\u5236\u7406\u8bba\uff09\u3001\u72af\u7f6a\u5b66\u53ca\u91d1\u878d\u7cfb\u7edf\u3002<\/span><\/p>\n


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

    \u63a7\u5236\u7406\u8bba\u4e00\u822c\u7684\u76ee\u7684\u662f\u501f\u7531\u63a7\u5236\u5668\u7684\u52a8\u4f5c\u8ba9\u7cfb\u7edf\u7a33\u5b9a\uff0c\u4e5f\u5c31\u662f\u7cfb\u7edf\u7ef4\u6301\u5728\u8bbe\u5b9a\u503c\uff0c\u800c\u4e14\u4e0d\u4f1a\u5728\u8bbe\u5b9a\u503c\u9644\u8fd1\u6643\u52a8\u3002\u7ef4\u6301\u8bbe\u5b9a\u503c\u4fdd\u6301\u5c0f\u8303\u56f4\u7a33\u5b9a\u751a\u81f3\u4e0d\u53d8\u7684\u63a7\u5236\u884c\u4e3a\u79f0\u4e3a\u63a7\u5236\u8c03\u8282\uff0c\u8bbe\u5b9a\u503c\u5feb\u901f\u53d8\u5316\uff0c\u5bf9\u4e8e\u8ddf\u8e2a\u901f\u5ea6\u52a0\u901f\u5ea6\u7b49\u7684\u63a7\u5236\u8981\u6c42\u8f83\u9ad8\u7684\u63a7\u5236\u884c\u4e3a\u79f0\u4e3a\u4f3a\u670d\u3002\u63a7\u5236\u7406\u8bba\u7684\u7814\u7a76\u7684\u4e00\u90e8\u5206\u7814\u7a76\u5bf9\u4e8e\u52a8\u529b\u7cfb\u7edf\u884c\u4e3a\u7684\u7814\u7a76\u4ea7\u751f\u4e86\u6df1\u8fdc\u7684\u5f71\u54cd\u3002<\/span><\/p>\n


    <\/p>\n

    \u904d\u5386\u7406\u8bba<\/span><\/strong><\/p>\n

    \u904d\u5386\u7406\u8bba Ergodic Theory \u662f\u6570\u5b66\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u5b83\u8d77\u6e90\u4e8e\u4e3a\u7edf\u8ba1\u529b\u5b66\u63d0\u4f9b\u57fa\u7840\u7684”\u904d\u5386\u5047\u8bbe”\u7814\u7a76\uff0c\u5e76\u4e0e\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u3001\u6982\u7387\u8bba\u3001\u4fe1\u606f\u8bba\u3001\u6cdb\u51fd\u5206\u6790\u3001\u6570\u8bba\u7b49\u6570\u5b66\u5206\u652f\u6709\u7740\u5bc6\u5207\u7684\u8054\u7cfb\u3002<\/span><\/p>\n


    <\/p>\n

    \u6cdb\u51fd\u5206\u6790<\/span><\/strong><\/span><\/p>\n

    \u6cdb\u51fd\u5206\u6790 Functional analysis \u662f\u6570\u5b66\u5206\u6790\u7684\u4e00\u4e2a\u5206\u652f\uff0c\u7814\u7a76\u5411\u91cf\u7a7a\u95f4\u548c\u4f5c\u7528\u4e8e\u5411\u91cf\u7a7a\u95f4\u7684\u7b97\u5b50\u3002\u5b83\u6e90\u4e8e\u5bf9\u51fd\u6570\u7a7a\u95f4\u7684\u7814\u7a76\uff0c\u7279\u522b\u662f\u5bf9\u51fd\u6570\u53d8\u6362\u7684\u7814\u7a76\uff0c\u4f8b\u5982\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u5fae\u79ef\u5206\u65b9\u7a0b\u7684\u7814\u7a76\u7b49\u3002\u6cdb\u51fd\u5206\u6790\u7684\u540d\u79f0\u201cFunctional Analysis\u201d\u4e2d\uff0c\u201cfunctional\u201d\u8fd9\u4e2a\u8bcd\u7684\u7528\u6cd5\u53ef\u4ee5\u8ffd\u6eaf\u5230\u53d8\u5206\u6cd5\uff0c\u4e5f\u5c31\u662f\u8bf4\u51fd\u6570\u7684\u53c2\u6570\u662f\u4e00\u4e2a\u51fd\u6570\u3002\u8fd9\u4e2a\u8bcd\u7684\u4f7f\u7528\u4e00\u822c\u88ab\u8ba4\u4e3a\u5f52\u529f\u4e8e\u6570\u5b66\u5bb6\u548c\u7269\u7406\u5b66\u5bb6Vito Volterra\uff0c\u5176\u521b\u7acb\u5f88\u5927\u7a0b\u5ea6\u4e0a\u5f52\u529f\u4e8e\u6570\u5b66\u5bb6Stefan Banach\u3002\u3002<\/span><\/p>\n


    <\/p>\n

    \u56fe\u52a8\u529b\u7cfb\u7edf<\/span><\/strong><\/p>\n

    \u56fe\u52a8\u529b\u7cfb\u7edf Graph dynamical systems(GDS) \u53ef\u4ee5\u7528\u6765\u63cf\u7ed8\u56fe\u6216\u7f51\u7edc\u4e0a\u53d1\u751f\u7684\u5404\u79cd\u8fc7\u7a0b\u3002\u56fe\u52a8\u529b\u7cfb\u7edf\u7684\u6570\u5b66\u548c\u8ba1\u7b97\u5206\u6790\u7684\u4e00\u4e2a\u4e3b\u8981\u4e3b\u9898\u662f\u5c06\u5176\u7ed3\u6784\u7279\u6027(\u4f8b\u5982\uff1a\u7f51\u7edc\u8fde\u63a5\u6027)\u4e0e\u5176\u6240\u4ea7\u751f\u7684\u5168\u5c40\u52a8\u529b\u5b66\u8054\u7cfb\u8d77\u6765\u3002<\/span><\/p>\n


    <\/p>\n

    \u6295\u5f71\u52a8\u529b\u7cfb\u7edf<\/span><\/strong><\/p>\n

    \u6295\u5f71\u52a8\u529b\u7cfb\u7edf Projected Dynamical Systems \u4e00\u79cd\u6570\u5b66\u7406\u8bba\uff0c\u7528\u4e8e\u7814\u7a76\u5c06\u89e3\u51b3\u65b9\u6848\u9650\u5236\u4e3a\u7ea6\u675f\u96c6\u7684\u52a8\u529b\u7cfb\u7edf\u7684\u884c\u4e3a\u3002\u8fd9\u95e8\u5b66\u79d1\u4e0e\u9759\u6001\u7406\u8bba\u4e2d\u7684\u6700\u4f18\u5316\u548c\u5e73\u8861\u95ee\u9898\u4ee5\u53ca\u52a8\u6001\u7406\u8bba\u4e2d\u7684\u5e38\u5fae\u5206\u65b9\u7a0b\u90fd\u6709\u8054\u7cfb\u548c\u5e94\u7528\u3002\u4e00\u4e2a\u6295\u5f71\u52a8\u529b\u7cfb\u7edf\u662f\u7531\u6295\u5f71\u5fae\u5206\u65b9\u7a0b\u7684\u6d41\u5f62\u7ed9\u5b9a\u7684\u3002\u901a\u8fc7\u5bf9\u6295\u5f71\u5fae\u5206\u65b9\u7a0b\u7684\u6d41\u5f62\u5206\u6790\uff0c\u7ed9\u51fa\u4e86\u4e00\u4e2a\u6295\u5f71\u52a8\u529b\u7cfb\u7edf\u7684\u8868\u8fbe\u5f0f\uff1a<\/span><\/p>\n


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    \u5176\u4e2dK\u4e3a\u7ea6\u675f\u96c6\u3002\u8fd9\u79cd\u5f62\u5f0f\u7684\u5fae\u5206\u65b9\u7a0b\u56e0\u5177\u6709\u4e0d\u8fde\u7eed\u7684\u5411\u91cf\u573a\u800c\u53d7\u5230\u8bb8\u591a\u7814\u7a76\u4eba\u5458\u7684\u6ce8\u610f\u3002<\/span><\/p>\n


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    \u7b26\u53f7\u52a8\u529b\u5b66<\/span><\/strong><\/p>\n

    \u7b26\u53f7\u52a8\u529b\u5b66 Symbolic Dynamics \u662f\u901a\u8fc7\u79bb\u6563\u7a7a\u95f4\u5bf9\u62d3\u6251\u6216\u5e73\u6ed1\u52a8\u529b\u5b66\u7cfb\u7edf\u8fdb\u884c\u5efa\u6a21\u7684\u65b9\u6cd5\uff0c\u8be5\u79bb\u6563\u7a7a\u95f4\u7531\u65e0\u9650\u7684\u62bd\u8c61\u7b26\u53f7\u5e8f\u5217\u7ec4\u6210\uff0c\u6bcf\u4e2a\u62bd\u8c61\u7b26\u53f7\u5bf9\u5e94\u4e8e\u7cfb\u7edf\u7684\u4e00\u4e2a\u72b6\u6001\uff0c\u5e76\u4e14\u52a8\u6001\uff08\u6f14\u5316\uff09\u7531\u79fb\u4f4d\u8fd0\u7b97\u7b26\u7ed9\u51fa\u3002<\/span><\/p>\n


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    \u7cfb\u7edf\u52a8\u529b\u5b66<\/span><\/strong><\/span><\/p>\n

    \u7cfb\u7edf\u52a8\u529b\u5b66 System Dynamics \u662f\u4e00\u79cd\u7406\u89e3\u7cfb\u7edf\u968f\u65f6\u95f4\u53d8\u5316\u884c\u4e3a\u7684\u65b9\u6cd5\u3002\u5b83\u662f\u7528\u6765\u5904\u7406\u5f71\u54cd\u6574\u4e2a\u7cfb\u7edf\u884c\u4e3a\u548c\u72b6\u6001\u7684\u5185\u90e8\u53cd\u9988\u56de\u8def\u548c\u65f6\u95f4\u5ef6\u8fdf\u7684\u65b9\u6cd5\u3002\u7cfb\u7edf\u52a8\u529b\u5b66\u4e0d\u540c\u4e8e\u5176\u4ed6\u7cfb\u7edf\u7814\u7a76\u65b9\u6cd5\u7684\u5730\u65b9\u5728\u4e8e\u5b83\u4f7f\u7528\u4e86\u53cd\u9988\u73af\u3001\u5b58\u91cf stocks\u548c\u6d41\u91cf flows\u7684\u5143\u7d20\u3002\u8fd9\u4e9b\u5143\u7d20\u6709\u52a9\u4e8e\u63cf\u8ff0\u770b\u4f3c\u7b80\u5355\u7684\u7cfb\u7edf\u5982\u4f55\u663e\u793a\u590d\u6742\u7684\u975e\u7ebf\u6027\u884c\u4e3a\u3002<\/span><\/p>\n


    <\/p>\n

    \u62d3\u6251\u52a8\u529b\u5b66<\/span><\/strong><\/p>\n

    \u62d3\u6251\u52a8\u529b\u5b66 Topological Dynamics \u662f\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u7684\u4e00\u4e2a\u5206\u652f\u3002\u5728\u62d3\u6734\u52a8\u529b\u5b66\u4e2d\uff0c\u52a8\u529b\u7cfb\u7edf\u7684\u5b9a\u6027\u6027\u8d28\u548c\u6e10\u8fd1\u6027\u8d28\u662f\u4ece\u4e00\u822c\u62d3\u6251\u5b66\u7684\u89c2\u70b9\u6765\u7814\u7a76\u7684\u3002<\/span><\/p>\n


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    6. \u5e94\u7528<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


    <\/p>\n

    \u5728\u8fd0\u52a8\u751f\u7269\u529b\u5b66\u4e2d\u7684\u5e94\u7528<\/span><\/strong><\/span><\/p>\n

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    <\/p>\n

    \u5728\u8ba4\u77e5\u79d1\u5b66\u4e2d\u7684\u5e94\u7528<\/span><\/strong><\/span><\/p>\n

    \u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u5df2\u7ecf\u88ab\u5e94\u7528\u4e8e\u795e\u7ecf\u79d1\u5b66\u548c\u8ba4\u77e5\u53d1\u5c55\u9886\u57df\uff0c\u7279\u522b\u662f\u5728\u8ba4\u77e5\u53d1\u5c55\u7684\u65b0\u76ae\u4e9a\u6770\u5b66\u6d3e neo-Piagetian\u4e2d\u3002\u4eba\u4eec\u76f8\u4fe1\uff0c\u7269\u7406\u5b66\u7406\u8bba\u6bd4\u53e5\u6cd5\u5b66 Syntax \u7406\u8bba\u548c\u4eba\u5de5\u667a\u80fd\u7406\u8bba\u66f4\u80fd\u4ee3\u8868\u8ba4\u77e5\u53d1\u5c55\u3002\u4eba\u4eec\u8fd8\u76f8\u4fe1\u5fae\u5206\u65b9\u7a0b\u662f\u4eba\u7c7b\u884c\u4e3a\u5efa\u6a21\u6700\u5408\u9002\u7684\u5de5\u5177\u3002\u4eba\u4eec\u8ba4\u4e3a\u5fae\u5206\u65b9\u7a0b\u53ef\u4ee5\u89e3\u91ca\u4e3a\u901a\u8fc7\u72b6\u6001\u7a7a\u95f4\u4ee3\u8868\u4e00\u4e2a\u4e3b\u4f53\u7684\u8ba4\u77e5\u8f68\u8ff9\u7684\u7b97\u5f0f\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u52a8\u529b\u5b66\u5bb6\u8ba4\u4e3a\u5fc3\u7406\u5b66\u5e94\u8be5\u662f\uff08\u6216\u8005\u5c31\u662f\uff09\uff08\u901a\u8fc7\u5fae\u5206\u65b9\u7a0b\uff09\u63cf\u8ff0\u5728\u4e00\u5b9a\u7684\u73af\u5883\u548c\u5185\u90e8\u538b\u529b\u4e0b\u7684\u4e3b\u4f53\u7684\u8ba4\u77e5\u548c\u884c\u4e3a\u7684\u5b66\u79d1\u3002\u6df7\u6c8c\u7406\u8bba\u5728\u76f8\u5173\u9886\u57df\u4e5f\u7ecf\u5e38\u88ab\u91c7\u7528\u3002<\/span><\/p>\n


    <\/p>\n

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    <\/p>\n

    \u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u6700\u8fd1\u8fd8\u88ab\u7528\u6765\u89e3\u91ca\u513f\u7ae5\u53d1\u5c55\u4e2d\u4e00\u4e2a\u957f\u671f\u6ca1\u6709\u7b54\u6848\u7684\u95ee\u9898\uff0c\u5373 A-not-B \u9519\u8bef\u3002<\/span><\/p>\n


    <\/p>\n

    \u5728\u7b2c\u4e8c\u8bed\u8a00\u53d1\u5c55\u4e2d\u7684\u5e94\u7528<\/span><\/strong><\/span><\/p>\n

    \u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u5728\u7b2c\u4e8c\u8bed\u8a00\u7814\u7a76\u4e2d\u7684\u5e94\u7528\u5f52\u529f\u4e8e Diane Larsen-Freeman\u6559\u6388\uff0c\u5979\u57281997\u5e74\u53d1\u8868\u7684\u4e00\u7bc7\u6587\u7ae0\u4e2d\u8ba4\u4e3a\uff0c\u7b2c\u4e8c\u8bed\u8a00\u5b66\u4e60\u5e94\u8be5\u88ab\u770b\u4f5c\u662f\u4e00\u4e2a\u5305\u62ec\u8bed\u8a00\u6d41\u5931\u548c\u8bed\u8a00\u4e60\u5f97\u5728\u5185\u7684\u53d1\u5c55\u8fc7\u7a0b\u3002\u5979\u5728\u6587\u7ae0\u4e2d\u8ba4\u4e3a\uff0c\u8bed\u8a00\u5e94\u8be5\u88ab\u770b\u4f5c\u662f\u4e00\u4e2a\u52a8\u6001\u7684\u3001\u590d\u6742\u7684\u3001\u975e\u7ebf\u6027\u7684\u3001\u6df7\u6c8c\u7684\u3001\u4e0d\u53ef\u9884\u77e5\u7684\u3001\u5bf9\u521d\u59cb\u6761\u4ef6\u654f\u611f\u7684\u3001\u5f00\u653e\u7684\u3001\u81ea\u7ec4\u7ec7\u7684\u3001\u53cd\u9988\u654f\u611f\u7684\u548c\u9002\u5e94\u6027\u7684\u52a8\u529b\u7cfb\u7edf\u3002<\/span><\/p>\n


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    7. \u76f8\u5173\u6982\u5ff5\u4e0e\u5b66\u8005<\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/section>\n

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


    <\/p>\n

    \u76f8\u5173\u6982\u5ff5<\/span><\/strong><\/span>
    <\/p>\n