{"id":40668,"date":"2023-02-13T21:50:59","date_gmt":"2023-02-13T13:50:59","guid":{"rendered":"https:\/\/swarma.org\/?p=40668"},"modified":"2023-02-13T21:50:59","modified_gmt":"2023-02-13T13:50:59","slug":"%e5%86%8d%e6%8e%a2%e6%b7%b7%e6%b2%8c%e8%be%b9%e7%bc%98%ef%bc%9a%e8%87%aa%e7%84%b6%e7%b3%bb%e7%bb%9f%e4%b8%8e%e4%ba%ba%e5%b7%a5%e7%b3%bb%e7%bb%9f%e4%b8%ad%e7%9a%84%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=40668","title":{"rendered":"\u518d\u63a2\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\uff1a\u81ea\u7136\u7cfb\u7edf\u4e0e\u4eba\u5de5\u7cfb\u7edf\u4e2d\u7684\u8ba1\u7b97\u539f\u7406"},"content":{"rendered":"
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\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\uff08edge of chaos\uff09\u662f\u4e00\u79cd\u4ecb\u4e8e\u6709\u5e8f\u548c\u65e0\u5e8f\uff08\u6df7\u6c8c\uff09\u4e4b\u95f4\u7684\u52a8\u6001\u673a\u5236\uff0c\u662f\u590d\u6742\u7cfb\u7edf\u79d1\u5b66\u7684\u6838\u5fc3\u6982\u5ff5\u3002\u751f\u547d\u7cfb\u7edf\u666e\u904d\u5b58\u5728\u67d0\u79cd\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\uff1f\u5982\u679c\u662f\uff0c\u90a3\u4e48\u8fd9\u4f1a\u662f\u81ea\u7ec4\u7ec7\u3001\u8fdb\u5316\u4ee5\u53ca\u590d\u6742\u7684\u81ea\u7136\u548c\u4eba\u5de5\u7cfb\u7edf\u6240\u987b\u9075\u5faa\u7684\u57fa\u672c\u539f\u5219\u5417\uff1f\u8fd9\u7bc7\u6587\u7ae0\u5c06\u56de\u987e\u4e00\u4e9b\u6587\u732e\uff0c\u4e3b\u8981\u5173\u6ce8\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u7684\u81ea\u7136\u7cfb\u7edf\u548c\u4eba\u5de5\u7cfb\u7edf\u4e2d\u8ba1\u7b97\u7684\u57fa\u672c\u539f\u7406\u300220\u4e16\u7eaa80\u5e74\u4ee3\uff0c\u8bfa\u66fc\u00b7\u5e15\u5361\u5fb7\u521b\u9020\u4e86\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u8fd9\u4e2a\u8bcd\u3002\u4ece\u90a3\u65f6\u8d77\uff0c\u201c\u9002\u5e94\u6df7\u6c8c\u8fb9\u7f18\u201d\u7684\u6982\u5ff5\u5728\u5f88\u591a\u9886\u57df\u90fd\u5f97\u5230\u4e86\u8bc1\u660e\u548c\u7814\u7a76\uff0c\u8fd9\u4e9b\u9886\u57df\u5185\u7684\u7b80\u5355\u7cfb\u7edf\u6216\u590d\u6742\u7cfb\u7edf\u90fd\u4f1a\u6536\u5230\u67d0\u79cd\u53cd\u9988\u3002\u9664\u4e86\u56de\u987e\u53e4\u4eca\u7684\u6587\u732e\u5916\uff0c\u672c\u6587\u8fd8\u5c06\u68b3\u7406\u5bf9\u8fd9\u4e00\u6982\u5ff5\u7684\u6279\u8bc4\u58f0\u3002<\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

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\u5173\u952e\u8bcd\uff1a\u6df7\u6c8c\u8fb9\u7f18\uff0c\u6df7\u6c8c<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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Christof Teuscher<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/span><\/p>\n

\u6731\u6b23\u6021<\/span> <\/span>| \u8bd1\u8005<\/strong><\/span><\/strong><\/span><\/span><\/p>\n

\u5218\u57f9\u6e90<\/span> <\/span>| \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/strong><\/span><\/span><\/p>\n

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


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Revisiting the edge of chaos: Again?<\/span><\/section>\n
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https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0303264722000806<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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1. \u56de\u5230\u6df7\u6c8c\u8fb9\u7f18\u7406\u8bba\u8d77\u70b9\uff1a\u4ece\u673a\u68b0\u8ba1\u7b97\u673a\u5230\u5143\u80de\u81ea\u52a8\u673a<\/span><\/strong><\/p>\n

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5. \u751f\u547d\u7cfb\u7edf\u5904\u4e8e\u4e34\u754c\u72b6\u6001\u5417\uff1f<\/span><\/strong><\/p>\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<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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1. \u56de\u5230\u6df7\u6c8c\u8fb9\u7f18\u7406\u8bba\u8d77\u70b9\uff1a<\/span><\/strong><\/strong><\/p>\n

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1665\u5e74\uff0c\u7f57\u4f2f\u7279\u00b7\u80e1\u514b<\/span>\uff08Robert Hooke\uff09<\/span>\u51fa\u7248\u4e86\u300a\u663e\u5fae\u672f\u300b<\/span>\uff08Micrographia<\/em>\uff09<\/span>\uff0c\u9996\u6b21\u5bf9\u690d\u7269\u7ec6\u80de\u4f5c\u51fa\u4e86\u8457\u540d\u7684\u63cf\u8ff0\u3002\u8ba1\u7b97\u7684\u5386\u53f2\u4e5f\u521a\u521a\u5f00\u59cb\u53d7\u5230\u4e00\u4e9b\u5173\u6ce8\uff1a\u5e15\u65af\u5361<\/span>\uff08Pas\u5143\u80de\u81ea\u52a8\u673al\uff09<\/span>\u57281642\u5e74\u8bbe\u8ba1\u4e86\u7b2c\u4e00\u4e2a\u53ef\u4ee5\u6267\u884c\u52a0\u6cd5\u548c\u51cf\u6cd5\u7684\u673a\u68b0\u8ba1\u7b97\u5668\u2014\u2014\u5e15\u65af\u5361\u6797\u3002\u540e\u6765\uff0c\u83b1\u5e03\u5c3c\u8328<\/span>\uff08Leibnitz\uff09<\/span>\u6539\u8fdb\u4e86\u5e15\u65af\u5361\u7684\u53d1\u660e\uff0c\u4f46\u76f4\u523019\u4e16\u7eaa20\u5e74\u4ee3\uff0cCharles Babbage\u624d\u8bbe\u8ba1\u51fa\u5dee\u5206\u673a\uff0c\u8fd9\u662f\u4e00\u79cd\u590d\u6742\u5f97\u591a\u7684\u673a\u68b0\u8ba1\u7b97\u5668\uff0c\u53ef\u4ee5\u5c06\u591a\u9879\u5f0f\u51fd\u6570\u5236\u6210\u8868\u683c\u3002\u4e4b\u540e\u53c8\u8fc7\u4e86\u5341\u591a\u5e74\uff0c\u76f4\u52301936\u5e74\u56fe\u7075<\/span>\uff08Alan M. Turing\uff09<\/span>\u5728\u4ed6\u7684\u8457\u540d\u8bba\u6587\u91cc\u5960\u5b9a\u4e86\u4e00\u4e9b\u201c\u73b0\u4ee3\u8ba1\u7b97\u201d\u7684\u5173\u952e\u57fa\u7840\uff0c\u5373\u6982\u5ff5\u56fe\u7075\u673a<\/span>\uff08TM\uff09<\/span>\u548c\u901a\u7528\u56fe\u7075\u673a<\/span>\uff08UTM\uff09\uff08\u56fe\u7075\uff0c1936\u5e74\u81f31937\u5e74\uff09<\/span>\u3002\u5728\u8fd9\u4e2a\u65f6\u95f4\u70b9\uff0c\u7ec6\u80de\u751f\u7269\u5b66\u9886\u57df\u4e5f\u53d6\u5f97\u4e86\u91cd\u5927\u8fdb\u5c55\uff0c\u4e0d\u5230\u4e00\u5e74\uff0cHans Adolf Krebs\u624d\u53d1\u73b0\u67e0\u6aac\u9178\u5faa\u73af\uff0c\u4e5f\u79f0\u4e3a\u4e09\u7fa7\u9178\u5faa\u73af\u6216\u514b\u96f7\u5e03\u65af\u5faa\u73af<\/span>\uff08Krebs\u548c\u7ea6\u7ff0\u900a\uff0c1937\uff09<\/span>\uff0c\u8fd9\u662f\u4e00\u7cfb\u5217\u53ef\u4ee5\u4f5c\u4e3a\u7ec6\u80de\u4e3b\u8981\u80fd\u91cf\u6765\u6e90\u7684\u5316\u5b66\u53cd\u5e94\u3002<\/span><\/section>\n

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\u7ec6\u80de\u751f\u7269\u5b66\u548c\u8ba1\u7b97\u7684\u878d\u5408\u76f8\u5f53\u81ea\u7136\u5730\u521b\u9020\u4e86\u751f\u7269\u8ba1\u7b97\u3001\u5206\u5b50\u8ba1\u7b97\u548c\u7ec6\u80de\u8ba1\u7b97\u9886\u57df\u3002\u5728\u56fe\u7075\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u667a\u80fd\u673a\u68b0<\/span>\uff08\u56fe\u7075\uff0c1969\uff09<\/span>\u548c\u5f62\u6001\u53d1\u751f<\/span>\uff08\u56fe\u7075\uff0c1952\uff09<\/span>\u4e2d\uff0c\u4ed6\u7b2c\u4e00\u4e2a\u4ecb\u7ecd\u4e86\u4e0a\u8ff0\u6982\u5ff5\u3002\u4e0d\u4e45\u4ee5\u540e, Liberman\u5728\u53d1\u5c55\u751f\u7269\u8ba1\u7b97\u7684\u8303\u5f0f\u548c\u201c\u7ec6\u80de\u4f5c\u4e3a\u5206\u5b50\u7535\u8111\u201d\u7684\u6982\u5ff5\u7684\u5de5\u4f5c\u4e2d\u6210\u4e3a\u5148\u950b\u3002\u5173\u4e8e\u8fd9\u4e2a\u4e3b\u9898\uff0c\u4ed6\u6700\u65e9\u7684\u5de5\u4f5c\u53ef\u4ee5\u8ffd\u6eaf\u52301972\u5e74\uff0c\u4ed6\u4ecb\u7ecd\u7ec6\u80de\u662f\u5206\u5b50\u8ba1\u7b97\u5668,\u5e76\u53ef\u4ee5\u4f7f\u7528\u5206\u5b50\u8bed\u8a00\u63a7\u5236\u81ea\u5df1<\/span>\uff08Liberman, 1972\uff09<\/span>\u3002\u4e4b\u540e\uff0c\u5728\u4ed61979\u5e74\u7684\u8bba\u6587<\/span>\uff08Liberman, 1979\uff09<\/span>\uff0cLiberman\u63cf\u8ff0\u4e86\u4ed6\u6240\u8c13\u7684\u5206\u5b50\u7ec6\u80de\u8ba1\u7b97\u5668 <\/span>(MCC) <\/span>\uff0c\u5e76\u5217\u51fa\u4e86\u66f4\u591a\u7684\u7ec6\u8282\u548c\u5b83\u7684\u57fa\u672c\u7279\u6027\u3002\u4ed6\u8fd8\u63d0\u51fa\uff0c\u201c\u5047\u5b9a\u6d3b\u7ec6\u80de\u9075\u5faa\u73b0\u5b9e\u6216\u4fe1\u606f\u7269\u7406\u5b66\u201d\u3002\u5728\u8fd9\u7bc7\u6587\u7ae0\u6700\u540e\uff0cMichael Conrad\u8bc4\u8bba\u9053\uff1a\u201cLiberman\u535a\u58eb\u63d0\u51fa\u4e86\u4e00\u4e2a\u4e0d\u53ef\u907f\u514d\u7684\u6709\u4e89\u8bae\u7684\u89c2\u70b9\uff0c\u5373\u751f\u547d\u7cfb\u7edf\u6240\u9700\u8981\u7684\u662f\u4e00\u79cd\u4fe1\u606f\u7269\u7406\u5b66\uff0c\u5b83\u53ef\u80fd\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u662f\u4ece\u666e\u901a\u7269\u7406\u5b66\u4fee\u6539\u800c\u6765\u7684\u3002\u201d<\/span>\uff08Liberman\uff0c1979\uff09<\/span>\u3002<\/span><\/section>\n

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Liberman 1972\u5e74\u7684\u89c2\u70b9\u5f15\u53d1\u4e86\u5173\u4e8e\u7269\u7406\u5b66\u3001\u751f\u7269\u5b66\u548c\u4fe1\u606f\u8bba\u4ea4\u53c9\u7684\u6709\u8da3\u95ee\u9898\uff0c\u5176\u4e2d\u4e00\u4e9b\u95ee\u9898\u81f3\u4eca<\/span>\uff08\u90e8\u5206\u6216\u5168\u90e8\uff09<\/span>\u4ecd\u672a\u5f97\u5230\u89e3\u7b54\u3002\u7269\u7406\u5b66\u548c\u751f\u7269\u5b66\u5b9a\u5f8b\u80fd\u4ece\u4fe1\u606f\u8bba\u4e2d\u63a8\u5bfc\u51fa\u6765\u5417\uff1f\u7269\u7406\u5b66\u548c\u751f\u7269\u5b66\u80fd\u53d1\u5c55\u65b0\u7684\u65b9\u5f0f\u5904\u7406\u4fe1\u606f\u5417\uff1f\u4ec0\u4e48\u662f\u751f\u7269\u4fe1\u606f\uff1f\u751f\u7269\u4fe1\u606f\u5904\u7406\u662f\u5426\u53d1\u751f\u5728\u67d0\u79cd\u201c\u751c\u871c\u70b9\u201d\u6216\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u2014\u2014\u4e00\u79cd\u4ecb\u4e8e\u6709\u5e8f\u4e0e\u6df7\u6c8c\u4e4b\u95f4\u7684\u52a8\u6001\u673a\u5236\uff1f\u5982\u679c\u662f\u8fd9\u6837\u7684\u8bdd\uff0c\u8fd9\u4e2a\u201c\u751c\u871c\u70b9\u201d\u662f\u5426\u662f\u81ea\u7ec4\u7ec7\u3001\u8fdb\u5316\u4ee5\u53ca\u590d\u6742\u7684\u7269\u7406\u3001\u751f\u7269\u548c\u4eba\u5de5\u7cfb\u7edf\u9002\u5e94\u73af\u5883\u7684\u57fa\u7840\uff1f\u9a71\u52a8\u7cfb\u7edf\u8fbe\u5230\u67d0\u4e9b\u201c\u751c\u871c\u70b9\u201d\u7684\u6743\u8861\u539f\u5219\u662f\u4ec0\u4e48\uff1f<\/span><\/section>\n

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20\u591a\u5e74\u540e\uff0cLiberman\u5df2\u7ecf\u627e\u5230\u4e86\u4e00\u4e9b\u7b54\u6848\u3002\u4f8b\u5982\uff0c\u4ed6\u57281996\u5e74\u4e0eMinina\u5408\u8457\u7684\u8bba\u6587<\/span>\uff08Liberman and Minina\uff0c1996\uff09<\/span>\u4e2d\uff0c\u63d0\u51fa\u4e86\u63cf\u8ff0\u751f\u7269\u7684\u56db\u4e2a\u7edf\u4e00\u539f\u5219\uff1a\u201c\u5efa\u8bbe\u2018\u65b0\u79d1\u5b66\u2019\u4f3c\u4e4e\u6709\u76ca\uff0c\u5b83\u901a\u8fc7\u5236\u5b9a\u57fa\u672c\u539f\u5219\uff0c\u4ee5\u7edf\u4e00\u7684\u89c2\u70b9\u63cf\u8ff0\u751f\u7269\u548c\u7269\u8d28\u4e16\u754c\u3002\u6211\u4eec\u8ba4\u4e3a\u8fd9\u4e9b\u539f\u5219\u662f\uff1a1.\u7528\u4e8e\u8ba1\u7b97\u548c\u6d4b\u91cf\u7684\u6700\u5c0f\u4ee3\u4ef7\u539f\u5219\uff1b2.\u6700\u4f18\u6027\u539f\u5219\uff1b3.\u6700\u5c0f\u4e0d\u53ef\u9006\u6027\u539f\u5219\uff1b4.\u56e0\u679c\u6027\u539f\u5219<\/span>\uff08\u65b0\u63aa\u8f9e\uff09<\/span>\u3002\u201d<\/span><\/section>\n

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\u867d\u7136Liberman\u4ece\u672a\u4f7f\u7528\u8fc7\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u8fd9\u4e2a\u8bcd\uff0c\u4f46\u4ed6\u548cMichael Conrad\u7684\u5f00\u521b\u6027\u5de5\u4f5c\u90fd\u6697\u793a\u4e86\u4e00\u4e2a\u6700\u4f73\u72b6\u6001\u6216\u201c\u751c\u871c\u70b9\u201d\uff0c\u5373\u751f\u547d\u7cfb\u7edf\u4e2d\u53d1\u751f\u4fe1\u606f\u5904\u7406\u7684\u5730\u65b9\uff0cConrad1989\u5e74\u7684\u8bba\u6587\u300a\u8111-\u673a\u53cd\u7c7b\u6bd4\u300b<\/span>\uff08Conrad\uff0c1989\uff09\uff08\u540e\u6765\u7531\u9f50\u683c\u52d2\uff08Zeigler\uff0c2002\uff09\u91cd\u65b0\u5ba1\u6821\uff09<\/span>\u4e2d\u53ef\u4ee5\u6e05\u695a\u5730\u53cd\u5e94\u8fd9\u4e2a\u89c2\u70b9\uff0c\u8fd9\u672c\u4e66\u91cc\u6982\u8ff0\u4e86\u8fdb\u5316\u6027<\/span>\uff08\u6216\u9002\u5e94\u6027\uff09<\/span>\u3001\u6548\u7387\u548c<\/span>\uff08\u7ed3\u6784\uff09<\/span>\u53ef\u7f16\u7a0b\u6027\u4e4b\u95f4\u7684\u6743\u8861\u539f\u5219\u3002\u7269\u7406\u9650\u5236\u5bfc\u81f4\u4e86\u8fd9\u6837\u7684\u6743\u8861\u3002\u201c\u4e0e\u5f53\u524d\u673a\u5668\u719f\u6089\u7684\u53ef\u7f16\u7a0b\u9886\u57df\u5b8c\u5168\u4e0d\u540c\uff0c\u6743\u8861\u539f\u5219\u610f\u5473\u7740\u4fe1\u606f\u5904\u7406\u7684\u9ad8\u6548\u7387\u3001\u9ad8\u9002\u5e94\u6027\u9886\u57df\u3002\u201d<\/span>\uff08Conrad\uff0c1989\uff09<\/span>\u3002<\/span><\/section>\n

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\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u5c06\u56de\u987e\u5728\u81ea\u7136\u7cfb\u7edf\u548c\u4eba\u5de5\u7cfb\u7edf\u4e2d\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u7684\u57fa\u672c\u8ba1\u7b97\u539f\u7406\u7684\u6587\u732e\u3002\u8fd9\u4e2a\u672f\u8bed\u662fNorman Packard\u572820\u4e16\u7eaa80\u5e74\u4ee3\u672b\u521b\u9020\u7684<\/span>\uff08Packard\uff0c1988\uff09<\/span>\u3002\u4ece\u90a3\u65f6\u8d77\uff0c\u201c\u9002\u5e94\u6df7\u6c8c\u8fb9\u7f18\u201d\u7684\u6982\u5ff5\u5728\u8bb8\u591a\u9886\u57df\u5f97\u5230\u4e86\u8bc1\u660e\u548c\u7814\u7a76\uff0c\u5728\u8fd9\u4e9b\u9886\u57df\u4e2d\uff0c\u7b80\u5355\u7cfb\u7edf\u548c\u590d\u6742\u7cfb\u7edf\u90fd\u63a5\u6536\u5230\u67d0\u79cd\u53cd\u9988\u3002\u9664\u4e86\u56de\u987e\u53e4\u4eca\u7684\u6587\u732e\u5916\uff0c\u6211\u4eec\u8fd8\u5c06\u56de\u987e\u5bf9\u8fd9\u4e00\u6982\u5ff5\u7684\u6279\u8bc4\u3002\u8bf7\u6ce8\u610f\uff0c\u672c\u6587\u4e0d\u662f\u5173\u4e8e\u6df7\u6c8c\u3001\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u548c\u8bb8\u591a\u5176\u4ed6\u4e0e\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u7406\u8bba\u76f8\u5173\u7684\u5b50\u9886\u57df\u3002\u6211\u4eec\u5c06\u53ea\u89e6\u53ca\u8fd9\u4e9b\u4e3b\u9898\u7684\u8fb9\u7f18\uff0c\u800c\u4e3b\u8981\u662f\u9075\u5faa\u201c\u6df7\u6c8c\u7684\u8fb9\u7f18\u201d\u7684\u6545\u4e8b\u7ebf\u3002<\/span><\/section>\n

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2. \u65e9\u671f\u6df7\u6c8c\u8fb9\u7f18\uff1a<\/span><\/strong><\/strong><\/p>\n

\u5143\u80de\u81ea\u52a8\u673a\u4e0e\u968f\u673a\u5e03\u5c14\u7f51\u7edc<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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 <\/span><\/section>\n
\u6df7\u6c8c\u8fb9\u7f18\u7684\u65e9\u671f\u7814\u7a76\u4e3b\u8981\u96c6\u4e2d\u5728\u5143\u80de\u81ea\u52a8\u673a<\/span>\uff08\u5143\u80de\u81ea\u52a8\u673a\uff09\uff08Toffoli and Margolus\uff0c1987\uff09<\/span>\u548c\u5176\u4ed6\u79bb\u6563\u52a8\u529b\u7cfb\u7edf\uff0c\u5982\u968f\u673a\u5e03\u5c14\u7f51\u7edc<\/span>\uff08RBN\uff09\uff08Kauffman\uff0c1969\uff09<\/span>\u3002\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u91cd\u70b9\u4ecb\u7ecd\u4e00\u4e9b\u5c06\u6df7\u6c8c\u8fb9\u7f18\u7814\u7a76\u5f15\u5411\u4e0d\u540c\u7684\u65b9\u5411\u7684\u65e9\u671f\u5de5\u4f5c\u3002<\/span><\/section>\n

<\/span><\/section>\n
1988\u5e74\uff0c\u5728Norman Packard\u51fa\u7248\u7684\u4e66\u4e2d\uff0c\u9898\u4e3a\u201c\u9002\u5e94\u6df7\u6c8c\u8fb9\u7f18\u201d\u7684\u7ae0\u8282\u4e2d\uff0c\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u4e00\u8bcd\u8bde\u751f<\/span>\uff08Packard\uff0c1988\u5e74\uff09<\/span>\u3002Packard\u63d0\u51fa\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u81ea\u9002\u5e94\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u4f7f\u7528\u9057\u4f20\u7b97\u6cd5<\/span>\uff08GA\uff09<\/span>\u6765\u8fdb\u5316\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219<\/span>\uff08Holland\uff0c1975\uff09<\/span>\u3002\u4ed6\u7684\u6a21\u62df\u8868\u660e\uff0c\u201c\u89c4\u5219\u7684\u7fa4\u4f53\u603b\u662f\u671d\u7740\u89c4\u5219\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u533a\u57df\u79fb\u52a8\uff0c\u8fd9\u4e2a\u533a\u57df\u6807\u5fd7\u7740\u6df7\u6c8c\u89c4\u5219\u548c\u975e\u6df7\u6c8c\u89c4\u5219\u4e4b\u95f4\u7684\u8fb9\u754c\u201d\u3002\u8fd9\u79cd\u884c\u4e3a\u53ef\u4ee5\u89e3\u91ca\u4e3a,\u9996\u5148, \u89c2\u5bdf\u5f97\u5230\u5728\u5143\u80de\u81ea\u52a8\u673a\u4e2d\u9700\u8981\u901a\u4fe1\u4ee5\u8fdb\u884c\u91cd\u8981\u8ba1\u7b97\u3002Packard\u4f7f\u7528\u5bc6\u5ea6\u5206\u7c7b\u4efb\u52a1\uff0c\u8be5\u4efb\u52a1\u7531\u5143\u80de\u81ea\u52a8\u673a\u81ea\u884c\u51b3\u5b9a\u521d\u59cb\u72b6\u6001\u4e2d\u201c1\u201d\u7684\u521d\u59cb\u5bc6\u5ea6\u662f\u5426\u5927\u4e8e50%\u3002\u5982\u679c\u5927\u4e8e50%\uff0c\u5bc6\u5ea6\u5206\u7c7b\u4efb\u52a1\u5c31\u8981\u6c42\u5143\u80de\u81ea\u52a8\u673a\u671d\u7740\u6240\u6709\u4f4d\u7f6e\u90fd\u662f1\u7684\u72b6\u6001\u6f14\u5316\uff1b\u5982\u679c\u5bc6\u5ea6\u5c0f\u4e8e50%\uff0c\u5c31\u8981\u6c42\u5143\u80de\u81ea\u52a8\u673a\u671d\u7740\u6240\u6709\u4f4d\u7f6e\u90fd\u662f0\u7684\u72b6\u6001\u6f14\u5316\u3002\u5355\u72ec\u770b\u6bcf\u4e00\u6b21\u5b9e\u9a8c\u90fd\u6ca1\u6709\u610f\u4e49\uff0c\u56e0\u4e3a\u6bcf\u6b21\u90fd\u80fd\u8ba1\u7b97\u51fa1\u7684\u5360\u6bd4\u3002\u7136\u800c\uff0c\u5143\u80de\u81ea\u52a8\u673a\u7684\u7ec6\u80de\u4ec5\u80fd\u770b\u89c1\u9644\u8fd1\u7684\u7ec6\u80de<\/span>\uff08\u4f8b\u5982\uff0c\u534a\u5f84\u4e3a3\uff09<\/span>\uff0c\u8fd9\u4f7f\u5f97\u8be5\u4efb\u52a1\u53d8\u5f97\u6709\u4ef7\u503c\uff0c\u56e0\u4e3a\u5b83\u8981\u6c42\u7ec6\u80de\u53ea\u8fdb\u884c\u5c40\u90e8\u901a\u4fe1\u800c\u8fbe\u5230\u5168\u5c40\u4e00\u81f4\u7684\u72b6\u6001\u3002\u7b2c\u4e8c\uff0c\u53ef\u4ee5\u76f4\u89c2\u5730\u7406\u89e3\uff0c\u6839\u672c\u4e0d\u4e0e\u90bb\u5c45\u901a\u4fe1<\/span>\uff08\u6216\u5f88\u5c11\u901a\u4fe1\uff09<\/span>\u7684\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219\u65e0\u6cd5\u89e3\u51b3\u5bc6\u5ea6\u4efb\u52a1\u3002\u5e15\u5361\u5fb7\u79f0\u8fd9\u4e9b\u89c4\u5219\u662f\u201c\u65e0\u6548\u7684\u201d\u3002\u6211\u4eec\u53ef\u4ee5\u8bf4\u8fd9\u4e2a\u7cfb\u7edf\u592a\u201c\u6b7b\u677f\u201d\u6216\u592a\u201c\u6709\u5e8f\u201d\u4e86\uff0c\u4e0d\u80fd\u505a\u4efb\u4f55\u6709\u7528\u7684\u4e8b\u60c5\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u89c4\u5b9a\u7684\u4ea4\u6d41\u592a\u591a\uff0c\u5219\u4efb\u4f55\u5c40\u90e8\u6270\u52a8\u5c06\u5f88\u5f71\u54cd\u5143\u80de\u81ea\u52a8\u673a\u7684\u72b6\u6001\uff0c\u8fd9\u4e5f\u5bfc\u81f4\u65e0\u6cd5\u89e3\u51b3\u624b\u5934\u7684\u4efb\u52a1\u3002Packard\u79f0\u8fd9\u4e9b\u89c4\u5219\u201c\u975e\u5e38\u6d3b\u8dc3\u201d\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u5b83\u4eec\u5c5e\u4e8e\u89c4\u5219\u7a7a\u95f4\u4e2d\u7684\u201c\u6df7\u6c8c\u201d\u72b6\u6001\u3002\u4ed6\u7684\u7ed3\u8bba\u662f\uff1a\u201c\u56e0\u6b64\uff0c\u53ef\u4ee5\u5408\u7406\u5730\u9884\u8ba1\uff0c\u4efb\u4f55\u9700\u8981\u8fd9\u79cd\u901a\u4fe1\u7684\u8ba1\u7b97\u90fd\u53ea\u80fd\u901a\u8fc7\u63a5\u8fd1\u6df7\u6c8c\u8fb9\u7f18\u7684\u89c4\u5219\u6765\u5b8c\u6210\u201d<\/span>\uff08Packard\uff0c1988\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u6709\u8da3\u7684\u662f\uff0c Wolfram\u57281984\u5e74\u53d1\u8868\u8fc7\u4e00\u7bc7\u5f88\u6709\u5f71\u54cd\u529b\u7684\u8bba\u6587<\/span>\uff08Wolfram\uff0c1984\uff09<\/span>\uff0c\u5176\u4e2d\u4ed6\u4e3a\u4e00\u7ef4\u5143\u80de\u81ea\u52a8\u673a\u5f15\u5165\u4e86\u56db\u4e2a\u4e0d\u540c\u7684\u666e\u9002\u7c7b\uff0c\u5e76\u63d0\u51fa4\u7c7b\u5143\u80de\u81ea\u52a8\u673a\u80fd\u591f\u8fdb\u884c\u666e\u9002<\/span>\uff08\u6216\u201c\u590d\u6742\u201d\uff09<\/span>\u8ba1\u7b97\u3002\u4f46Packard\u5e76\u6ca1\u6709\u5f15\u7528\u3002\u867d\u7136Wolfram\u548cLangton\u57281986\u5e74\u53d1\u8868\u7684\u9898\u4e3a\u201c\u7528\u5143\u80de\u81ea\u52a8\u673a\u7814\u7a76\u4eba\u5de5\u751f\u547d\u201d<\/span>\uff08Langton\uff0c1986\uff09<\/span>\u7684\u8bba\u6587\u4e2d\uff0c\u751a\u81f3\u90fd\u6ca1\u6709\u4f7f\u7528\u8fc7\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u8fd9\u4e2a\u672f\u8bed\uff0c\u4f46\u4ed6\u4eec\u8fd8\u662f\u4e3a\u5b83\u7684\u7814\u7a76\u5960\u5b9a\u4e86\u8bb8\u591a\u57fa\u7840\u3002\u4f8b\u5982\uff0cLangton\u63d0\u51fa\u4e86\u4e00\u4e2a\u7531\u865a\u62df\u72b6\u6001\u673a<\/span>\uff08VSM\uff09<\/span>\u7ec4\u6210\u7684\u4eba\u5de5\u751f\u7269\u5316\u5b66\u6837\u672c\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u201c\u5206\u5b50\u64cd\u4f5c\u5668\u201d\u3002\u4ed6\u53ef\u80fd\u6697\u6307\u6df7\u6c8c\u8fb9\u7f18\uff0c\u4ed6\u6307\u51fa\u201c\u5176\u4e2d\u4e00\u4e2a\u7cfb\u7edf\u7684\u4f8b\u5b50\uff0c\u4f3c\u4e4e\u5f88\u597d\u5730\u5e73\u8861\u4e86\u9759\u6b62\u548c\u6df7\u6c8c\u2026\u2026\u4e3a\u4e86\u52a8\u6001\u5730\u7ef4\u6301\u8fd9\u79cd\u5e73\u8861\uff0c\u5fc5\u987b\u6709\u67d0\u79cd\u6709\u5e8f\u7684\u81ea\u6211\u8c03\u8282\u673a\u5236\u3002\u201d \u4f46\u66f4\u503c\u5f97\u6ce8\u610f\u7684\u4e5f\u8bb8\u662fLangton\u901a\u8fc7\u5143\u80de\u81ea\u52a8\u673a\u5728\u6a21\u62df\u751f\u7269\u5316\u5b66\u548c\u4eba\u5de5\u5206\u5b50\u4e4b\u95f4\u5efa\u7acb\u7684\u8054\u7cfb\u3002\u201c\u751f\u7269\u5316\u5b66\u7814\u7a76\u751f\u547d\u5982\u4f55\u4ece\u65e0\u751f\u547d\u5206\u5b50\u7684\u76f8\u4e92\u4f5c\u7528\u4e2d\u6d8c\u73b0\u2026\u2026\u5143\u80de\u81ea\u52a8\u673a\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5f88\u597d\u7684\u4eba\u5de5\u5b87\u5b99\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u5176\u4e2d\u5d4c\u5165\u865a\u62df\u81ea\u52a8\u673a\u5f62\u5f0f\u7684\u4eba\u5de5\u5206\u5b50\u201d <\/span>(Langton, 1986)<\/span>\u3002<\/span><\/section>\n

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\u51e0\u5e74\u540e\uff0cLangton\u5b8c\u5168\u8d76\u4e0a\u4e86\u6df7\u6c8c\u8fb9\u7f18\u7684\u6f6e\u6d41\uff0c\u53d1\u8868\u4e86\u4e00\u7bc7\u73b0\u5728\u4ecd\u88ab\u5927\u91cf\u5f15\u7528\u7684\u6587\u7ae0<\/span>\uff08Langton\uff0c1990\uff09<\/span>\u3002\u8fd9\u7bc7\u6587\u7ae0\u5c55\u73b0\u51fa\u4ed6\u7684\u89c2\u70b9\u4e0ePackard\u7684\u89c2\u70b9\u76f8\u540c\uff1a\u76f4\u89c9\u4e0a\u8bb2\uff0c\u63a5\u8fd1\u6df7\u6c8c\u8fb9\u7f18\u7684\u89c4\u5219\u5177\u6709\u6700\u597d\u7684\u4fe1\u606f\u901a\u4fe1\u80fd\u529b\uff0c\u56e0\u6b64\u6700\u9002\u5408\u8ba1\u7b97\u3002Langton\u518d\u6b21\u4f7f\u7528\u4e86\u7b80\u5355\u3001\u7edf\u4e00\u548c\u540c\u6b65\u5143\u80de\u81ea\u52a8\u673a\u7684\u6846\u67b6\uff1a\u201c\u672c\u6587\u4ecb\u7ecd\u4e86\u5143\u80de\u81ea\u52a8\u673a\u7684\u7814\u7a76\uff0c\u5b83\u8868\u660e\u76f8\u53d8\u9644\u8fd1\u662f\u652f\u6301\u5b9e\u73b0\u4fe1\u606f\u4f20\u8f93\u3001\u5b58\u50a8\u548c\u4fee\u6539\u7684\u6700\u4f73\u6761\u4ef6\u3002\u201d \u6587\u7ae0\u7684\u6700\u540e\uff0cLangton\u6307\u51fa\uff1a\u201c\u7cfb\u7edf\u5728\u76f8\u53d8\u9644\u8fd1\u8868\u73b0\u51fa\u4e00\u7cfb\u5217\u7684\u884c\u4e3a\uff0c\u8fd9\u4e9b\u884c\u4e3a\u975e\u5e38\u597d\u5730\u53cd\u6620\u4e86\u8ba1\u7b97\u73b0\u8c61\u5b66\uff0c\u6211\u4eec\u8ba4\u4e3a\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4f4d\u52a8\u529b\u5b66\u884c\u4e3a\u8c31\u4e2d\u5904\u4e8e\u76f8\u53d8\u7684\u8ba1\u7b97\u5b9a\u4e49\u4e3a\u5904\u4e8e\u2018\u6df7\u6c8c\u8fb9\u7f18\u2019\u201d<\/span>\uff08Langton\uff0c1990\uff09<\/span>\u3002Langton\u4f7f\u7528\u4e86\u53c2\u6570\ud835\udf06<\/span><\/span>\uff08\u6700\u521d\u5728Langton\uff081986\uff09\u4e2d\u5f15\u5165\uff09<\/span>\uff0c\u8be5\u53c2\u6570\u7528\u4e8e\u4ece\u6700\u540c\u8d28\u5230\u6700\u5f02\u8d28\u89c4\u5219\u8868\u63a2\u7d22\u548c\u8868\u5f81\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219\u7a7a\u95f4\u7684\u65b9\u6cd5\u3002\u7136\u540e\u4ed6\u8bf4\u660e\u4e86\u53c2\u6570\ud835\udf06<\/span>\u4e5f\u53ef\u4ee5\u652f\u6301Wolfram\u7684\u5de5\u4f5c\uff0c\u5e76\u5c06Wolfram\u7684\u5143\u80de\u81ea\u52a8\u673a\u56db\u7c7b\u548c\u4ed6\u81ea\u5df1\u7684\u7a7a\u95f4\u8fde\u63a5\u8d77\u6765\u3002<\/span><\/section>\n

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Langton\u5728\u95ee\u9898\u90e8\u5206\u63d0\u51fa\u4e86\u63d0\u51fa\u4e86\u4e24\u70b9\uff0c\u4e0e\u672c\u6587\u975e\u5e38\u76f8\u5173\uff1a<\/span><\/section>\n

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1. \u4ed6\u60f3\u77e5\u9053\u4ed6\u7684\u5de5\u4f5c\u4e0eBak\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u6709\u4f55\u5173\u7cfb<\/span>\uff08Bak et al.\uff0c1988\u5e74\uff09<\/span>\u3002<\/span><\/section>\n

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2. \u4ed6\u6307\u51fa\uff0c\u76f8\u53d8\u73b0\u8c61\u5728\u6d3b\u7ec6\u80de\u4e2d\u968f\u5904\u53ef\u89c1\u3002<\/span><\/section>\n

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\u7b2c\u4e8c\uff0c\u8ba9\u6211\u4eec\u56de\u5230Stuart Kauffman 1969\u5e74\u7684\u8bba\u6587<\/span>\uff08Kauffman\uff0c1969\uff09<\/span>\uff0c\u5728\u8fd9\u7bc7\u8bba\u6587\u4e2d\uff0c\u4ed6\u5f15\u5165\u4e86\u6b63\u5f0f\u9057\u4f20\u7f51\u7edc-\u4e5f\u79f0\u4e3a\u968f\u673a\u5e03\u5c14\u7f51\u7edc<\/span>\uff08RBN\uff09<\/span>\uff0cNK\u7f51\u7edc\u6216NK\u6a21\u578b\uff0c\u4f5c\u4e3a\u7531\u4e8c\u8fdb\u5236\u201c\u5f00-\u5173\u201d\u57fa\u56e0\u7ec4\u6210\u7684\u9057\u4f20\u8c03\u63a7\u7f51\u7edc\u7684\u6a21\u578b\uff0c\u7528\u4e8e\u7814\u7a76\u7ec6\u80de\u63a7\u5236\u8fc7\u7a0b\u3002\u5728\u5176\u6700\u7b80\u5355\u548c\u539f\u59cb\u7684\u5f62\u5f0f\u4e2d\uff0c\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u662f\u7531\ud835\udc41\u4e2a\u81ea\u52a8\u673a<\/span>\uff08\u6216\u8282\u70b9\uff09<\/span>\u7ec4\u6210\u7684\u79bb\u6563\u52a8\u529b\u7cfb\u7edf\uff0c\u5176\u4e2d\u6bcf\u4e2a\u8282\u70b9\u4ece\u5176\u4ed6\u968f\u673a\u9009\u62e9\u7684K\u4e2a\u8282\u70b9\u63a5\u6536\u8f93\u5165\u3002\u7ed3\u679c\u662f\uff0c\u6bcf\u4e2a\u8282\u70b9\u5e73\u5747\u5177\u6709\ud835\udc3e\u4e2a\u5230\u5176\u5b83\u8282\u70b9\u7684\u8f93\u51fa\u3002\u6bcf\u4e2a\u8282\u70b9\u90fd\u662f\u5e03\u5c14\u53d8\u91cf\uff0c\u53ea\u6709\u4e24\u79cd\u53ef\u80fd\u7684\u72b6\u6001\uff1a{0\uff0c1}\u3002\u800c\u52a8\u529b\u5b66\u6ee1\u8db3<\/sub>\uff0c\u5176\u4e2dF=\uff08f<\/span>1<\/sub>\uff0c\u2026\uff0cf<\/span>i<\/sub>\uff0c\u2026\uff0cf<\/span>N<\/sub>\uff09\uff0c\u5e76\u4e14\u6bcf\u4e2afi<\/sub>\u90fd\u7531\u4ece\ud835\udc41\u4e2a\u8282\u70b9\u96c6\u5408\u4e2d\u968f\u673a\u9009\u62e9\u7684\u8f93\u5165Ki<\/sub>\u7684\u67e5\u627e\u8868\u6765\u8868\u793a\u3002\u6700\u521d\uff0cKi<\/sub>\u4e2a\u90bb\u5c45\u548c\u67e5\u627e\u8868\u88ab\u968f\u673a\u5206\u914d\u7ed9\u6bcf\u4e2a\u8282\u70b9\uff1a<\/sub>\u3002\u6bcf\u4e2a\u8282\u70b9\u7684\u72b6\u6001<\/sub>\u7528\u76f8\u5e94\u7684\u5e03\u5c14\u51fd\u6570\u66f4\u65b0\uff1a<\/span><\/section>\n

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\u6bcf\u4e2a\u8282\u70b9\u7528\u5176\u76f8\u5e94\u7684\u5e03\u5c14\u51fd\u6570\u540c\u6b65\u66f4\u65b0\uff1a<\/sub>\u3002\u7ecf\u5178\u7684\u540c\u6b65RBN\u7684\u72b6\u6001\u6570\u76ee\u6709\u9650\uff0c\u5e76\u4e14\u5728\u4e00\u5b9a\u6570\u76ee\u7684\u65f6\u95f4\u6b65\u4e4b\u540e\uff0c\ud835\udc47\u5c06\u843d\u5165\u56fa\u5b9a\u6216\u5faa\u73af\u5438\u5f15\u5b50\u3002<\/span><\/section>\n

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Kauffman\u7814\u7a76\u4e86\u4e09\u5927\u7c7b\u9057\u4f20\u7f51\u7edc\u7684\u5468\u671f\u548c\u6270\u52a8\uff1a\uff081\uff09\u5168\u8fde\u901a\ud835\udc3e =\ud835\udc41\uff0c\uff082\uff09\ud835\udc3e= 1\uff0c\uff083\uff09\ud835\udc3e= 2\u3002\u4ed6\u5f97\u51fa\u7ed3\u8bba\uff0c\u5168\u8fde\u901a\u7f51\u7edc\uff08K=N\uff09\u5728\u751f\u7269\u5b66\u4e0a\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\ud835\udc3e=1\u7ea7\u7f51\u7edc\u9700\u8981\u5730\u7403\u4e0a\u4efb\u4f55\u751f\u7269\u90fd\u4e0d\u5177\u5907\u7684\u5faa\u73af\uff0c\ud835\udc3e=2\u7ea7\u7f51\u7edc\u5728\u751f\u7269\u5b66\u4e0a\u662f\u5408\u7406\u7684\u3002Kauffman\u8ba4\u4e3a\uff0c\u751f\u7269\u4f53\u4e2d\u57fa\u56e0\u7f51\u7edc\u7684\u53c2\u6570\u662f\u901a\u8fc7\u8fdb\u5316\u8c03\u6574\u7684\uff0c\u56e0\u6b64\u5b83\u4eec\u5c06\u5728\u63a5\u8fd1\u6df7\u6c8c\u8fb9\u7f18\u7684\u5173\u952e\u9636\u6bb5\u8fd0\u884c\u3002\u66f4\u5e7f\u6cdb\u5730\u8bf4\uff0c\u4ed6\u7684\u7814\u7a76\u7ed3\u679c\u8868\u660e\uff0c\u6df7\u6c8c\u8fb9\u7f18\u7684\u751f\u7269\u7f51\u7edc\u8868\u73b0\u51fa\u7a33\u5b9a\u6027\u3001\u53ef\u8fdb\u5316\u6027\u548c\u4fe1\u606f\u5904\u7406\u6548\u7387\uff0c\u8fd9\u4e0eConrad\u63d0\u51fa\u7684\u6743\u8861\u539f\u5219\u4e00\u81f4<\/span>\uff08Conrad\uff0c1989\uff09<\/span>\u3002Derrida \u548c Pomeau\u82b1\u4e86\u5c06\u8fd120\u5e74\u7684\u65f6\u95f4\uff0c\u4ee5\u53ca\u968f\u540e\u7684\u5728\u90a3\u4e2a\u4e16\u7eaa\u672b\u7684\u8bb8\u591a\u5176\u4ed6\u4eba\uff0c\u624d\u5f00\u59cb\u4ece\u66f4\u6570\u5b66\u5316\u7684\u89d2\u5ea6\u5206\u6790\u5f84\u5411\u57fa\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Derrida and Pomeau\uff0c1986\uff09<\/span>\u3002<\/span><\/section>\n

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Kauffman\u5728\u6587\u7ae0\u7684\u7ed3\u5c3e\u4f5c\u4e86\u5982\u4e0b\u9648\u8ff0\uff1a\u201c\u7531\u5927\u7684\u3001\u968f\u673a\u7ec4\u5408\u7684\u4e8c\u8fdb\u5236\u5143\u7d20\u7ec4\u6210\u7684\u7f51\u7edc\u5177\u6709\u7b80\u5355\u3001\u7a33\u5b9a\u548c\u6709\u5e8f\u7684\u7279\u6027\u3002\u5927\u81ea\u7136\u5229\u7528\u4e86\u8fd9\u79cd\u53ef\u80fd\u7684\u548c\u53ef\u9760\u7684\u7cfb\u7edf\uff0c\u6765\u521b\u9020\u8fdb\u5316\u548c\u4fdd\u62a4\u5176\u540e\u4ee3\u201d<\/span>\uff08Kaufman, 1969\uff09<\/span>\u3002<\/span><\/section>\n

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\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\uff1a\u65e9\u671f\u5173\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u7684\u5de5\u4f5c\u4e3b\u8981\u96c6\u4e2d\u5728\u79bb\u6563\u52a8\u529b\u7cfb\u7edf\u4e0a\uff0c\u5e76\u63d0\u4f9b\u4e86\u8bc1\u636e\u8bc1\u660e\uff1a\u5728\u8fd9\u79cd\u52a8\u529b\u7cfb\u7edf\u4e2d\u590d\u6742\u7684\u52a8\u529b\u5b66\u51fa\u73b0\u5728\u67d0\u4e9b\u76f8\u53d8\u9644\u8fd1\uff0c \u201c\u4f9d\u8d56\u4e8e\u5904\u7406\u4fe1\u606f\u7684\u57fa\u672c\u80fd\u529b\u201d<\/span>\uff08Langton\uff0c1990\uff09<\/span>\u3002<\/span><\/section>\n

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\u6545\u4e8b\u7ee7\u7eed\u4e4b\u524d\uff0c\u6211\u4eec\u5148\u6765\u542c\u4e00\u542c\u6279\u8bc4\u7684\u58f0\u97f3\u3002<\/span><\/section>\n

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3. \u6279\u8bc4\u7684\u58f0\u97f3<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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Mitchell\u7b49\u4eba\u7684\u6587\u7ae0\u603b\u662f\u88ab\u5f15\u4f5c\u5bf9\u6df7\u6c8c\u8fb9\u7f18\u7684\u6279\u8bc4<\/span>\uff08Mitchell et al., 1993\uff09<\/span>\u3002\u7136\u800c\uff0c\u4e8b\u5b9e\u5e76\u975e\u5982\u6b64\u3002\u8fd9\u4e9b\u6587\u7ae0\u66f4\u50cf\u662f\u5bf9Packard\u7684\u53d1\u73b0<\/span>\uff08Packard\uff0c1988\uff09<\/span>\u7684\u5177\u4f53\u6279\u8bc4\uff0c\u8fd9\u4e9b\u53d1\u73b0\u6d89\u53ca\u7edf\u4e00\u7684\u3001\u4e00\u7ef4\u7684\u3001\u540c\u6b65\u7684\u5143\u80de\u81ea\u52a8\u673a\u7684\u8fdb\u5316\u3001\u52a8\u529b\u5b66\u548c\u8ba1\u7b97\u80fd\u529b\u3002Mitchell\u7b49\u4eba\u8bd5\u56fe\u901a\u8fc7\u8fdb\u884c\u4e00\u7ec4\u7c7b\u4f3c\u7684\u5b9e\u9a8c\u6765\u590d\u73b0Packard\u7684\u7ed3\u679c\u3002\u4e0d\u5e78\u7684\u662f\uff0cPackard\u7684\u8bba\u6587\u9057\u6f0f\u4e86\u76f8\u5f53\u591a\u7684\u6280\u672f\u7ec6\u8282\uff0c\u8fd9\u8feb\u4f7fMitchell\u7b49\u4eba\u5bf9\u51e0\u4e2a\u53c2\u6570\u505a\u51fa\u4e86\u201c\u5408\u7406\u201d\u7684\u5047\u8bbe\u3002\u4f46\u9057\u61be\u7684\u662f\uff0cMitchell\u7b49\u4eba\u6839\u672c\u65e0\u6cd5\u91cd\u73b0Packard\u7684\u7ed3\u679c\uff1a\u201c\u6211\u4eec\u7684\u5b9e\u9a8c\u4ea7\u751f\u4e86\u5b8c\u5168\u4e0d\u540c\u7684\u7ed3\u679c\uff0c\u6211\u4eec\u8ba4\u4e3a\u5bf9\u539f\u59cb\u7ed3\u679c\u7684\u89e3\u91ca\u662f\u4e0d\u6b63\u786e\u7684\u201d<\/span>\uff08Mitchell et al., 1993\uff09<\/span>\u3002\u867d\u7136\u4ed6\u4eec\u89c2\u5bdf\u5230\u66f4\u590d\u6742\u7684\u89c4\u5219\u5728\u6f14\u53d8\uff0c\u4f46\u8fd9\u4e9b\u89c4\u5219\u4f3c\u4e4e\u5e76\u4e0d\u5b58\u5728\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u3002\u4ed6\u4eec\u8fdb\u4e00\u6b65\u6307\u51fa\u201c\u2026\u2026\u6211\u4eec\u4e0d\u77e5\u9053\u662f\u4ec0\u4e48\u539f\u56e0\u9020\u6210\u6211\u4eec\u7684\u7ed3\u679c\u4e0e\u539f\u59cb\u5b9e\u9a8c\u7ed3\u679c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002\u201d<\/span><\/section>\n

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Mitchell\u7b49\u4eba\u5728\u4ed6\u4eec\u7684\u4e00\u822c\u6027\u8ba8\u8bba\u4e2d\u660e\u786e\u6307\u51fa\uff0c\u201c\u6211\u4eec\u7ed9\u51fa\u7684\u7ed3\u679c\u5e76\u6ca1\u6709\u53cd\u9a73\u8fd9\u4e2a\u5047\u8bbe\uff1a\u8ba1\u7b97\u80fd\u529b\u4e0e\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219\u7a7a\u95f4\u4e2d\u7684\u76f8\u53d8\u76f8\u5173\u201d\u3002\u8fd9\u4e00\u5047\u8bbe\u540e\u6765\u5f97\u5230\u4e86\u4e00\u4e9b\u4f5c\u8005\u7684\u8bc1\u5b9e\u3002<\/span><\/section>\n

<\/span><\/section>\n
1995\u5e74\uff0cGutowitz\u548cLangton\u91cd\u65b0\u68c0\u67e5\u4e86\u662f\u5426\u5b58\u5728\u6df7\u6c8c\u7684\u8fb9\u7f18\uff0c\u4ee5\u53ca\u6f14\u5316\u662f\u5426\u80fd\u591f\u5f15\u5bfc\u7cfb\u7edf\u5230\u8fbe\u6df7\u6c8c\u8fb9\u7f18<\/span>\uff08Gutowitz and Langton\uff0c1995\uff09<\/span>\u3002\u4ed6\u4eec\u8ba4\u4e3a\uff0c\u9700\u8981\u4e00\u79cd\u65b0\u7684\u590d\u6742\u6027\u8861\u91cf\u6807\u51c6\u6765\u786e\u5b9a\u8fd9\u4e9b\u95ee\u9898\uff0c\u5e76\u8ba4\u4e3a\u8d8b\u540c\u65f6\u95f4\u662f\u4e00\u4e2a\u9002\u5f53\u7684\u6307\u6807\u3002\u901a\u8fc7\u4f7f\u7528\u5e73\u5747\u573a\u65b9\u6cd5\uff0c\u4ed6\u4eec\u8bc1\u660e\u4e86\uff1a\u968f\u7740\u6f14\u5316\uff0c\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219\u786e\u5b9e\u53d8\u5f97\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u800c\u4e14\u5173\u952e\u89c4\u5219\u7684\u5e73\u5747\u6536\u655b\u901f\u5ea6\u6bd4\u975e\u5173\u952e\u89c4\u5219\u8981\u6162\u3002Kaneko\u548cSuzuki<\/span>\uff081994\uff09<\/span>\u4ee5\u53caSuzuki\u548cKaneko<\/span>\uff081994\uff09<\/span>\u4f7f\u7528\u903b\u8f91\u65af\u8482\u56fe\u786e\u5b9a\u4e86\u6df7\u6c8c\u8fb9\u7f18\uff0c\u5f97\u51fa\u4e86\u7c7b\u4f3c\u7684\u7ed3\u679c\u3002\u4ed6\u4eec\u8fd8\u53d1\u73b0\uff0c\u5728\u9002\u5f53\u7684\u6761\u4ef6\u4e0b\uff0c\u6f14\u5316\u8fc7\u7a0b\u786e\u5b9e\u4f1a\u9a71\u4f7f\u4e00\u4e2a\u7cfb\u7edf\u8d70\u5411\u6df7\u6c8c\u8fb9\u7f18\u3002<\/span><\/section>\n

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1997\u5e74\uff0cSiper\u5728\u4ed6\u7684\u4e66\u4e2d\u62a5\u544a\u8bf4\uff0c\u4ed6\u83b7\u5f97\u4e86\u652f\u6301Mitchell\u7b49\u4eba\u7684\u7ed3\u679c<\/span>\uff08Siper\uff0c1997\uff09<\/span>\u3002\u4ed6\u4f7f\u7528\u81ea\u5df1\u7684\u201c\u5143\u80de\u7f16\u7a0b\u7b97\u6cd5\u201d\u8fdb\u884c\u5b9e\u9a8c\uff0c\u8be5\u7b97\u6cd5\u4f9d\u8d56\u4e8e\u5c40\u90e8\u9002\u5e94\u6027\u6d4b\u91cf<\/span>\uff08\u4e0e\u8fdb\u5316\u7b97\u6cd5\u4e2d\u7684\u5168\u5c40\u6d4b\u91cf\u76f8\u53cd\uff09<\/span>\u3002Siper\u53d1\u73b0\u7684\u89c4\u5219\u96c6\u4e2d\u5728\ud835\udf06= 0.5\u9644\u8fd1\uff0c\u5927\u90e8\u5206\u57280.45-0.55\u4e4b\u95f4\uff0c\u8fd9\u4e0eMitchell\u7b49\u4eba\u7684\u7814\u7a76\u7ed3\u679c\u4e00\u81f4\u3002\u5bc6\u5ea6\ud835\udf06\u4efb\u52a1\u7684\u503c\u53ef\u80fd\u63a5\u8fd10.5\u3002\u5728\u4ed6\u7684\u5b9e\u9a8c\u4e2d\uff0c\u66f4\u590d\u6742\u7684\u89c4\u5219\u518d\u6b21\u6f14\u5316\u51fa\u6765\uff0c\u4f46\u5bf9\u4e8ePackard\u6709\u5173\u6df7\u6c8c\u8fb9\u7f18\u7684\u7ed3\u679c\uff0c\u4eba\u4eec\u5b58\u5728\u5206\u6b67\u3002<\/span><\/section>\n

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\u5728\u7ed3\u675f\u672c\u8282\u65f6\uff0c\u6211\u4eec\u518d\u6b21\u5f3a\u8c03Mitchell\u7b49\u4eba\u7684\u6587\u7ae0\u662f\u5bf9Packard\u5b9e\u9a8c\u7684\u6279\u8bc4\uff0c\u4e5f\u662f\u4e00\u6b21\u5931\u8d25\u7684\u5c1d\u8bd5\u3002\u4ed6\u4eec\u7684\u8bba\u70b9\u548c\u53d1\u73b0\u5b8c\u5168\u4f9d\u8d56\u4e8e\u7edf\u4e00\u7684\u5143\u80de\u81ea\u52a8\u673a\uff0c\u800c\u7edf\u4e00\u5143\u80de\u81ea\u52a8\u673a\u7684\u89c4\u5219\u662f\u901a\u8fc7\u4f7f\u7528\u9057\u4f20\u7b97\u6cd5\u8fdb\u5316\u800c\u6765\u7684\u3002\u8fd9\u7bc7\u6587\u7ae0\u6ca1\u6709\u8d28\u7591\u6df7\u6c8c\u8fb9\u7f18\u7684\u5e7f\u6cdb\u5b58\u5728\uff0c\u4e5f\u6ca1\u6709\u8d28\u7591\u6f14\u5316\uff0c\u6216\u5176\u4ed6\u9002\u5e94\u6027\u53cd\u9988\u673a\u5236\uff0c\u53ef\u4ee5\u63a8\u52a8\u7cfb\u7edf\u8d70\u5411\u6df7\u6c8c\u8fb9\u7f18\u3002\u56e0\u6b64\uff0c\u5f15\u7528\u8fd9\u7bc7\u6587\u7ae0\u4f5c\u4e3a\u5bf9\u6df7\u6c8c\u8fb9\u7f18\u7684\u6279\u8bc4\uff0c\u5c31\u50cf\u5b83\u7ecf\u5e38\u505a\u7684\u90a3\u6837\u2014\u2014\u662f\u8bef\u5bfc\u3002\u4f8b\u5982\uff0c\u7ef4\u57fa\u767e\u79d1\u5173\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u7684\u6587\u7ae0\u786e\u5b9e\u6307\u51fa\uff0c\u201c\u7136\u800c\uff0cMelanie Mitchell\u548c\u5176\u4ed6\u4eba\u5bf9\u8fd9\u4e00\u60f3\u6cd5\u7684\u666e\u904d\u6027\u548c\u91cd\u8981\u6027\u63d0\u51fa\u4e86\u8d28\u7591\u201d<\/span>\uff08Wikipedia\uff0c2022\uff09<\/span>\u3002\u8fd9\u662f\u4e00\u4e2a\u4e0d\u51c6\u786e\u7684\u9648\u8ff0\uff0c\u5e76\u4e14\u4e0d\u53cd\u6620Mitchell\u7b49\u4eba\u7684\u7ed3\u8bba\u3002<\/span><\/section>\n

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\u4e8b\u5b9e\u4e0a\uff0c\u5728\u968f\u540e\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0cMitchell\u7b49\u4eba<\/span>\uff08Mitchell et al.\uff0c1994\uff09<\/span>\u5305\u542b\u4e86\u4e00\u4e9b\u989d\u5916\u7684\u8bba\u70b9\u548c\u89c2\u70b9\uff0c\u518d\u6b21\u5f3a\u8c03\u4e86\u201c\u2026\u2026\u6211\u4eec\u7684\u7814\u7a76\u5e76\u4e0d\u6392\u9664\u5c06\u6765\uff0c\u5728\u5143\u80de\u81ea\u52a8\u673a\u7684\u80cc\u666f\u4e0b\uff0c\u6709\u4eba\u80fd\u5bf9\u201c\u6df7\u6c8c\u8fb9\u7f18\u201d\u4e00\u8bcd\u4f5c\u51fa\u4e25\u683c\u800c\u6709\u7528\u7684\u5b9a\u4e49\u3002\u5b83\u4eec\u4e5f\u4e0d\u6392\u9664\u53d1\u73b0\u6df7\u6c8c\u8fb9\u7f18\u4e0e\u5143\u80de\u81ea\u52a8\u673a\u7684\u8ba1\u7b97\u80fd\u529b\u589e\u5f3a\u6709\u5173\u3002\u6700\u540e\uff0c\u5b83\u4eec\u4e0d\u6392\u9664\u81ea\u9002\u5e94\u7cfb\u7edf\u6f14\u5316\u5230\u8fd9\u6837\u7684\u52a8\u6001\u533a\u57df\uff0c\u4ee5\u4fbf\u5229\u7528\u90a3\u91cc\u56fa\u6709\u7684\u8ba1\u7b97\u80fd\u529b\u3002\u201d\u518d\u65e9\u4e9b\u65f6\u5019\uff0cCrutchfield\u548cYoung\u5c31\u63d0\u4f9b\u4e86\u5927\u91cf\u8bc1\u636e<\/span>\uff08Crutchfield and Young \uff0c1990\uff09<\/span>\u3002<\/span><\/section>\n

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4. \u6df7\u6c8c\u8fb9\u7f18\u5982\u4f55\u51c6\u786e\u5b9a\u4e49\uff1f<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5230\u76ee\u524d\u4e3a\u6b62\uff0c\u6211\u4eec\u8fd8\u6ca1\u6709\u6b63\u5f0f\u5b9a\u4e49\u6df7\u6c8c\u8fb9\u7f18\u3002\u73b0\u5728\u8ba9\u6211\u4eec\u6765\u8c08\u8c08\u8fd9\u4e2a\u95ee\u9898\u3002\u6211\u4eec\u5c06\u63a2\u8ba8\u4e24\u79cd\u4e3b\u8981\u7684\u65b9\u6cd5\u6765\u754c\u5b9a\u4e00\u822c\u6240\u8ba4\u4e3a\u7684\u6df7\u6c8c\u8fb9\u7f18\uff1a\uff081\uff09Derrida\u7684\u6a21\u62df\u9000\u706b\u548c\uff082\uff09Lyapunov\u6307\u6570\u3002<\/span><\/section>\n

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\u6d4b\u91cf<\/span>\uff08\u901a\u5e38\u5f88\u5c0f\u7684\uff09<\/span>\u5c40\u90e8\u6270\u52a8<\/span>\uff08\u53c8\u79f0\u201c\u635f\u4f24\u201d\u6216\u566a\u58f0\uff09<\/span>\u5728\u52a8\u529b\u7cfb\u7edf\u4e2d\u7684\u4f20\u64ad\u662f\u4e00\u79cd\u786e\u5b9a\u7cfb\u7edf\u5904\u4e8e\u4f55\u79cd\u72b6\u6001\u7684\u65e2\u5b9a\u65b9\u5f0f\u3002\u4e3a\u6b64\uff0c\u521b\u5efa\u7cfb\u7edf\u7684\u4e24\u4e2a\u526f\u672c\uff0c\u5e76\u5728\u5176\u4e2d\u4e00\u4e2a\u7cfb\u7edf\u4e2d\u5f15\u5165\u4e00\u4e9b\u6270\u52a8\u3002\u7136\u540e\u968f\u65f6\u95f4\u6bd4\u8f83\u4e24\u4e2a\u72b6\u6001\u8f68\u8ff9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff1a\uff081\uff09\u5f53\u7cfb\u7edf\u5904\u4e8e<\/span>\uff08\u786e\u5b9a\u6027\uff09<\/span>\u6df7\u6c8c\u72b6\u6001\u65f6\uff0c\u6270\u52a8\u4f1a\u6269\u6563\uff1b\uff082\uff09\u5982\u679c\u7cfb\u7edf\u5904\u4e8e\u6709\u5e8f<\/span>\uff08\u6216\u201c\u51bb\u7ed3\u201d\uff09<\/span>\u533a\uff0c\u6270\u52a8\u5c06\u6d88\u5931\uff1b\u4ee5\u53ca\uff083\uff09\u5982\u679c\u7cfb\u7edf\u5904\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u7684\u4e34\u754c\/\u590d\u6742\u72b6\u6001\uff0c\u5219\u6270\u52a8\u5c06\u4fdd\u6301\u5728\u6052\u5b9a\u5927\u5c0f\u3002\u56e0\u6b64\uff0c\u786e\u5b9a\u6df7\u6c8c\u8fb9\u7f18\u7684\u4e3b\u8981\u95ee\u9898\u662f\uff1a\u6270\u52a8\u662f\u6d88\u5931\u3001\u7ef4\u6301\u8fd8\u662f\u589e\u957f\uff1f\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u52a8\u529b\u7cfb\u7edf\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u5ea6\u662f\u591a\u5c11\uff1f\u5728\u4e34\u754c\u9636\u6bb5\uff0c\u5373\u6df7\u6c8c\u8fb9\u7f18\uff0c\u6270\u52a8\u5c06\u5728\u957f\u65f6\u95f4\u548c\u7a7a\u95f4\u5c3a\u5ea6\u4e0a\u4f20\u64ad\uff0c\u65e2\u4e0d\u8870\u51cf\u4e5f\u4e0d\u653e\u5927\u3002<\/span><\/section>\n

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Kauffman\u5728\u4ed61969\u5e74\u7684\u8bba\u6587\u4e2d\u7814\u7a76\u4e86\u6270\u52a8\uff0c\u5e76\u4f7f\u7528\u5b83\u4eec\u5bf9\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u8fdb\u884c\u5206\u7c7b<\/span>\uff08Kauffman\uff0c1969\uff09<\/span>\u30021986\u5e74\uff0cDerrida\u548cPomeau\u63d0\u51fa\u4e86\u6a21\u62df\u9000\u706b\u6cd5<\/span>\uff08AA\uff09<\/span>\uff0c\u8fd9\u662f\u4e00\u79cd\u5e73\u5747\u573a\u65b9\u6cd5<\/span>\uff08Derrida and Pomeau\uff0c1986\uff09<\/span>\uff0c\u540e\u6765\u53c8\u6709\u4eba\u8fdb\u884c\u4e86\u6269\u5c55\uff0c\u4f8b\u5982\uff1a<\/span>(Sol\u00e9 and Luque, 1995, Luque and Sol\u00e9, 1997)<\/span>\u3002Derrida\u548cPomeau\u7684\u5206\u6790\u8868\u660e\uff0c\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\uff0c\u5373\uff1a\u5f53\u7f51\u7edc\u89c4\u6a21\u8d8b\u4e8e\u65e0\u7a77\u5927\u65f6\uff0c\u53ef\u4ee5\u7cbe\u786e\u786e\u5b9a\u4e34\u754c\u70b9\u3002\u5bf9\u4e8eKauffman\u7684\u968f\u673a\u7f51\u7edc\uff0c\u53d1\u73b0\u5b83\u4eec\u5728\u7a00\u758f\u4e34\u754c\u8fde\u901a\u5ea6\u65f6\u8868\u73b0\u51fa\u52a8\u6001\u6709\u5e8f-\u65e0\u5e8f\u8f6c\u53d8\u3002\u7136\u800c\uff0c\u5728\u5b9e\u9645\u95ee\u9898\u7684\u5e94\u7528\u4e2d\uff0c\u70ed\u529b\u5b66\u6781\u9650\u901a\u5e38\u4e0d\u662f\u5f88\u91cd\u8981\u3002\u8fd1\u671f\u7684\u5de5\u4f5c\u66f4\u5173\u6ce8\u6709\u9650\u5927\u5c0f\u7f29\u653e\uff0c\u8fd9\u65e2\u7528\u4e8e\u968f\u673a\u5e03\u5c14\u7f51\u7edc<\/span>\uff08RBN\uff09<\/span>\uff0c\u4e5f\u7528\u4e8e\u968f\u673a\u9608\u503c\u7f51\u7edc<\/span>\uff08RTN\uff09<\/span>\uff0c\u53ef\u53c2\u89c1 <\/span>(Rohlf and Bornholdt, 2002, R\u00e4m\u00f6 et al., 2006, Samuelsson and Socolar, 2006, Lu and Teuscher, 2014, Ishii et al., 2019, Rohlf et al., 2007, Goudarzi et al., 2012) <\/span>\u3002\u6211\u4eec\u7a0d\u540e\u5c06\u770b\u5230\u5982\u4f55\u901a\u8fc7\u81ea\u7ec4\u7ec7\u5b9e\u73b0\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u7684\u5173\u952e\u8fde\u63a5\u3002<\/span><\/section>\n

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\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\ud835\udf06\u6d4b\u91cf\u52a8\u529b\u7cfb\u7edf<\/span>\uff08\u5728\u76f8\u7a7a\u95f4\u4e2d\u7684\uff09<\/span>\u4e24\u4e2a\u8f68\u8ff9\u4e4b\u95f4\u7684\u5206\u79bb\u901f\u7387\u3002\u56e0\u6b64\uff0c\u8be5\u6307\u6570\u80fd\u591f\u6d4b\u91cf\u4e0d\u7a33\u5b9a\u7a0b\u5ea6\uff0c\u5e76\u786e\u5b9a\u6df7\u6c8c\u8fb9\u7f18\u3002\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u63cf\u8ff0\u7cfb\u7edf\u7684\u77ed\u671f\u884c\u4e3a\uff0c\u800c\u6700\u5927\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570<\/span>\uff08MLE\uff09<\/span>\u5219\u63cf\u8ff0\u7cfb\u7edf\u7684\u957f\u671f\u52a8\u6001\u3002\u4e00\u4e2a\u6b63\u7684<\/span>\uff08\u6700\u5927\uff09<\/span>\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u8868\u660e\u7cfb\u7edf\u5bf9\u521d\u59cb\u6761\u4ef6\u654f\u611f\uff0c\u56e0\u6b64\u5904\u4e8e\u6df7\u6c8c\u72b6\u6001\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\ud835\udf06\uff1c<\/span>0\uff0c\u5219\u7cfb\u7edf\u662f\u7a33\u5b9a\u7684\u6216\u6709\u5e8f\u7684\u3002\u5982\u679c\u4e00\u4e2a\u52a8\u529b\u7cfb\u7edf\u7684\u6700\u5927\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u4e3a0\uff0c\u90a3\u4e48\u5b83\u4f1a\u88ab\u8ba4\u4e3a\u5904\u4e8e\u6df7\u6c8c\u7684\u4e34\u754c\u72b6\u6001\u7684\u3002<\/span><\/section>\n

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\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u4e5f\u53ef\u4ee5\u4ece\u8bf8\u5982CAs\u548cRBNs\u7b49\u79bb\u6563\u7cfb\u7edf\u4e2d\u88ab\u5bfc\u51fa\uff0c\u53ef\u53c2\u89c1 <\/span>(Bagnoli et al., 1992, Luque and Sol\u00e9, 2000)<\/span>\u3002\u503c\u5f97\u6307\u51fa\u7684\u662f\uff0c\u6df7\u6c8c\u7406\u8bba\u7684\u8bb8\u591a\u5de5\u4f5c\u90fd\u662f\u57fa\u4e8e\u8fde\u7eed\u548c\u65e0\u9650\u7a7a\u95f4\u7684\u5047\u8bbe\uff0c\u6211\u4eec\u5728\u8fd9\u91cc\u5c31\u4e0d\u8ba8\u8bba\u4e86\u3002<\/span><\/section>\n

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\u6700\u540e\u4f46\u4e5f\u5f88\u91cd\u8981\u7684\u662f\uff0c\u5b9a\u4e49\u590d\u6742\u6027\u662f\u4ec0\u4e48\u53c8\u4e0d\u662f\u4ec0\u4e48\uff0c\u8fd9\u4ecd\u7136\u662f\u4e00\u4e2a\u5f00\u653e\u7684\uff0c\u6216\u8005\u8bf4\u81f3\u5c11\u662f\u4e00\u4e2a\u6709\u4e89\u8bae\u7684\u95ee\u9898\u3002Sol\u00e9\u7b49\u4eba\u6307\u51fa\uff1a\u201c\u5df2\u7ecf\u63d0\u51fa\u4e86\u51e0\u79cd<\/span>\uff08\u590d\u6742\u6027\u7684\uff09<\/span>\u5b9a\u4e49\uff0c\u5b83\u4eec\u90fd\u5171\u6709\u4e00\u4e2a\u76f4\u89c2\u6982\u5ff5\uff0c\u5373\u590d\u6742\u6027\u65e2\u4e0d\u662f\u5b8c\u5168\u6709\u5e8f\u7684\uff0c\u4e5f\u4e0d\u662f\u5b8c\u5168\u65e0\u5e8f\u7684\u201d (Sol\u00e9 et al., 1996)\u3002<\/span><\/section>\n

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5. \u751f\u547d\u7cfb\u7edf\u5904\u4e8e\u4e34\u754c\u72b6\u6001\u5417\uff1f<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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 <\/span><\/section>\n
\u5982\u4e0a\u6587\u6240\u63d0\u5230\u7684\uff0c Kauffman\u662f\u7b2c\u4e00\u4e2a\u5ba3\u79f0\u5e76\u8bc1\u660e\uff1a\u751f\u547d\u7cfb\u7edf\uff0c\u7279\u522b\u662f\u57fa\u56e0\u8c03\u63a7\u7f51\u7edc\uff0c\u662f\u5728\u6709\u5e8f\u4e0e\u6df7\u6c8c\u4e4b\u95f4\u7684\u4e34\u754c\u52a8\u529b\u5b66\u673a\u5236\u4e2d\u8fd0\u884c\u7684<\/span>\uff08Kauffman\uff0c1969\uff09<\/span>\u3002Kauffman\u7684\u5047\u8bbe\u4e4b\u4e00\u662f\uff0c\u7ec6\u80de\u7c7b\u578b\u5bf9\u5e94\u4e8eKauffman \u968f\u673a\u5e03\u5c14\u7f51\u7edc\u4e2d\u7684\u72b6\u6001\u5faa\u73af\u5438\u5f15\u5b50\u3002Kauffman\u6bd4Packard\u66f4\u8fdb\u4e00\u6b65\uff0cPackard\u8ba4\u4e3a\u4ed6\u7684\u5143\u80de\u81ea\u52a8\u673a\u89c4\u5219\u662f\u81ea\u7136\u9009\u62e9\u7684\u7ed3\u679c\u3002Kauffman\u7684\u7814\u7a76\u7ed3\u679c\u662f\uff1a\u9057\u4f20\u8c03\u63a7\u7f51\u7edc\u7684\u6027\u8d28\u662f\u5185\u5728\u52a8\u6001\u8fc7\u7a0b\u7684\u7ed3\u679c\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ece\u90a3\u65f6\u8d77\uff0c\u6709\u5145\u5206\u7684\u8bc1\u636e\u8868\u660e\uff1a\u51c6\u9759\u6001\u975e\u5e73\u8861\u6001\u751f\u547d\u7269\u8d28\u5728\u63a5\u8fd1\u6216\u7b49\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u7684\u67d0\u79cd\u4e34\u754c\u72b6\u6001\u4e0b\u8fd0\u884c\uff0c\u800c\u4e34\u754c\u72b6\u6001\u662f\u5728\u4e0d\u65ad\u5e73\u8861\u4e4b\u540e\u51fa\u73b0\u7684\u3002\u76f4\u89c2\u4e0a\uff0c\u8fd9\u5f88\u6709\u9053\u7406\uff0c\u56e0\u4e3a\u751f\u547d\u548c\u975e\u751f\u547d\u7cfb\u7edf\u5728\u5bf9\u73af\u5883\u4f5c\u51fa\u53cd\u5e94\u65f6\u90fd\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u76f8\u53d8<\/span> (Griffiths and Wheeler, 1970, Jacobs and Frenkel, 2017) <\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u540e\u6587\uff0c\u6211\u4eec\u5c06\u63d0\u5230\u4e00\u4e9b\u7279\u5b9a\u7684\u520a\u7269\uff0c\u4ee5\u5f3a\u8c03\u751f\u547d\u7cfb\u7edf\u4e34\u754c\u6027\u7684\u6982\u5ff5\u3002<\/span><\/section>\n

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\u5728Packard\u7684\u6df7\u6c8c\u8fb9\u7f18\u8bba\u6587\u53d1\u8868\u540e\u4e0d\u4e45\uff0cIto\u548cGunji\u63d0\u51fa\u4e86\u66f4\u591a\u7684\u8bc1\u636e\uff0c\u8bc1\u660e\u81ea\u7ec4\u7ec7\u4f5c\u4e3a\u4e00\u79cd\u8fdb\u5316\u8fc7\u7a0b\uff0c\u63a8\u52a8\u7740\u751f\u547d\u7cfb\u7edf\u8d70\u5411\u6df7\u6c8c\u8fb9\u7f18\u3002\u4ed6\u4eec\u8fd8\u5047\u8bbe\u4ed6\u4eec\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u662fBak\u7684\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\u7684\u4e00\u79cd\u63a8\u5e7f\u5f62\u5f0f<\/span>\uff08Ito and Gunji, 1994\uff09<\/span>\u3002<\/span><\/section>\n

<\/span><\/section>\n
2005\u5e74\uff0cShmulevich\u7b49\u4eba <\/span>(2005) <\/span>\u9996\u6b21\u8bc1\u660e\u4e86\u201c\u2026\u2026HeLa\u7ec6\u80de\u7684\u57fa\u672c\u9057\u4f20\u7f51\u7edc\u4f3c\u4e4e\u5728\u6709\u5e8f\u72b6\u6001\u4e0b\u6216\u5728\u6709\u5e8f\u4e0e\u6df7\u6c8c\u7684\u8fb9\u754c\u4e0a\u8fd0\u884c\uff0c\u4f46\u4f3c\u4e4e\u4e0d\u662f\u6df7\u6c8c\u7684\u3002\u201dKesseli\u548cYli-Harja\u63d0\u51fa\u4e86\u4e00\u79cd\u7814\u7a76\u57fa\u56e0\u8c03\u63a7\u7f51\u7edc\u5173\u952e\u6027\u7684\u65b0\u65b9\u6cd5\uff1a\u201c\u8be5\u65b9\u6cd5\u662f\u7b2c\u4e00\u6b21\u4f7f\u7528\u751f\u7269\u5b66\u6d4b\u91cf\u6570\u636e\uff0c\u6765\u91cf\u5316\u7ec6\u80de\u662f\u5426\u52a8\u6001\u6709\u5e8f\u3001\u4e34\u754c\u6216\u6df7\u6c8c\u7684\u5c1d\u8bd5\u4e4b\u4e00\u201d<\/span> (R\u00e4m\u00f6 et al., 2006)<\/span>\u3002Nykter et al.<\/span> (2008) <\/span>\u4f7f\u7528\u4e86\u5de8\u566c\u7ec6\u80de\u7684\u57fa\u56e0\u8868\u8fbe\u6570\u636e\uff0c\u53d1\u73b0\u5176\u52a8\u529b\u5b66\u81f3\u5173\u91cd\u8981\u3002Hanel \u7b49\u4eba <\/span>(2010) <\/span>\u8868\u660e\uff0c\u4ed6\u4eec\u7528\u4f5c\u751f\u7269\u53cd\u5e94\u7f51\u7edc\u6a21\u578b\u7684\u6781\u6700\u5c0f\u975e\u7ebf\u6027<\/span>\uff08MNL\uff09<\/span>\u7cfb\u7edf\u4e5f\u662f\u5982\u6b64\u3002<\/span><\/section>\n

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Torres-Sosa \u7b49\u4eba<\/span> (2012)<\/span> \u8ba8\u8bba\u4e86\uff1a\u57fa\u56e0\u7f51\u7edc\u5982\u4f55\u771f\u6b63\u8fbe\u5230\u4e34\u754c\u884c\u4e3a\uff1f\u8fd9\u4ecd\u7136\u662f\u4e00\u4e2a\u6709\u70b9\u96be\u4ee5\u6349\u6478\u7684\u5f00\u653e\u6027\u95ee\u9898\u3002\u4ed6\u4eec\u63d0\u51fa\u4e86\u201c\u2026\u2026\u4e00\u79cd\u8fdb\u5316\u6a21\u578b\uff0c\u5176\u4e2d\u4e34\u754c\u6027\u81ea\u7136\u5730\u4ece\u53ef\u8fdb\u5316\u6027\u7684\u4e24\u4e2a\u57fa\u672c\u7ec4\u6210\u4e4b\u95f4\u7684\u5e73\u8861\u6d8c\u73b0\u800c\u51fa\uff1a\u7a81\u53d8\u4e0b\u7684\u8868\u578b\u4fdd\u5b88\u548c\u8868\u578b\u521b\u65b0\u201d\u201c\u2026\u2026\u6211\u4eec\u7684\u7ed3\u679c\u8868\u660e\uff0c\u6269\u5c55\u65b0\u8868\u578b<\/span>\uff08\u521b\u65b0\uff09<\/span>\u4e0e\u4fdd\u7559\u73b0\u6709\u8868\u578b<\/span>\uff08\u4fdd\u7559\uff09<\/span>\u4e4b\u95f4\u7684\u8fd9\u79cd\u76f8\u4e92\u4f5c\u7528\uff0c\u8db3\u4ee5\u5bfc\u81f4\u79cd\u7fa4\u4e2d\u6240\u6709\u7f51\u7edc\u5411\u4e34\u754c\u72b6\u6001\u8fdb\u5316\u3002\u201d<\/span><\/section>\n

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\u867d\u7136Mora\u548cBialek\u6ca1\u6709\u63d0\u5230\u6df7\u6c8c\u8fb9\u7f18\uff0c\u4f46\u4ed6\u4eec\u7684\u6587\u7ae0\u6709\u95ee\u9053\uff1a\u201c\u751f\u547d\u7cfb\u7edf\u662f\u5426\u5904\u4e8e\u4e34\u754c\u72b6\u6001\uff1f\u201d <\/span>(Mora and Bialek, 2011)<\/span>\u3002\u4ed6\u4eec\u8ba8\u8bba\u4e86\uff0c\u5728\u5e7f\u6cdb\u7684\u751f\u547d\u7cfb\u7edf\u4e2d\u4e34\u754c\u6027\u7684\u5b9e\u9a8c\u8bc1\u636e\uff0c\u5305\u62ec\u86cb\u767d\u8d28\u7f51\u7edc\u3001\u795e\u7ecf\u7f51\u7edc\u548c\u9e1f\u7fa4\u3002\u201c\u8bf1\u4eba\u7684\u53ef\u80fd\u6027\u662f\uff0c\u8bb8\u591a\u7cfb\u7edf\u5e76\u4e0d\u6df1\u5904\u4e8e\u4e00\u4e2a\u76f8\u6216\u53e6\u4e00\u4e2a\u76f8\uff0c\u800c\u662f\u5728\u81ea\u7136\u53c2\u6570\u7a7a\u95f4\u7684\u4e34\u754c\u8868\u9762\u9644\u8fd1\u4fdd\u6301\u5e73\u8861\u3002\u201d<\/span><\/section>\n

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\u4eca\u5929\uff0c\u4ecd\u7136\u6709\u4e00\u4e2a\u534a\u5f00\u653e\u7684\u95ee\u9898\uff1a\u751f\u547d\u7cfb\u7edf\u7a76\u7adf\u662f\u5982\u4f55\u8fbe\u5230\u4e34\u754c\u72b6\u6001\u7684\uff1f\u56e0\u4e3a\u4e34\u754c\u72b6\u6001\u5f80\u5f80\u662f\u6574\u4e2a\u53c2\u6570\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5f88\u5c0f\u7684\u533a\u57df<\/span>\uff08\u5982\u679c\u4e0d\u662f\u4e00\u4e2a\u70b9\u7684\u8bdd\uff09<\/span>\u3002\u5927\u591a\u6570\u8bc1\u636e\u8868\u660e\uff0c\u8fd9\u662f\u4e00\u4e2a\u53cd\u9988\u673a\u5236\u548c\u5e73\u8861\u6f14\u5316\u7684\u7ec4\u5408<\/span> (Ulanowicz, 2002, Conrad, 1989) <\/span>\u3002<\/span><\/section>\n

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6. \u6df7\u6c8c\u8fb9\u7f18\u7814\u7a76\u7684\u5168\u76db\u65f6\u671f<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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 <\/span><\/section>\n
Kauffman\u572860\u5e74\u4ee3\u672b\u5f00\u59cb\u4e86\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u7684\u7814\u7a76<\/span>\uff08Kauffman\uff0c1969\uff09<\/span>\uff0c\u800c\u7406\u8bba\u5206\u6790\u7684\u5168\u76db\u65f6\u671f\u76f4\u5230\u65b0\u4e16\u7eaa\u521d\u624d\u5f00\u59cb\u3002\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u8db3\u591f\u7b80\u5355\u53ef\u4ee5\u5f62\u5f0f\u5316\u548c\u5206\u6790\uff0c\u4f46\u53c8\u8db3\u591f\u590d\u6742\u9976\u6709\u8da3\u5473\uff0c\u5bf9\u8bb8\u591a\u7814\u7a76\u4eba\u5458\u6765\u8bf4\u662f\u4e00\u4e2a\u5b8c\u7f8e\u7684\u6e38\u4e50\u573a\u3002\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u73b0\u4ee3\u5de5\u5177\u4e0e\u65b0\u51fa\u73b0\u7684\u65e0\u7a77\u65e0\u5c3d\u7684\u8ba1\u7b97\u8d44\u6e90\u76f8\u7ed3\u5408\uff0c\u4f7f\u8be5\u9886\u57df\u84ec\u52c3\u53d1\u5c55\u4e86\u8bb8\u591a\u5e74\u3002<\/span><\/section>\n

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\u7269\u7406\u5b66\u5bb6\u4e00\u81f4\u90fd\u5bf9\u5c0f\u578b\u7cfb\u7edf\u611f\u5174\u8da3\uff0c\u5982logistic\u6620\u5c04,\u6216\u81ea\u7ec4\u7ec7\u6f14\u5316\u5230\u6df7\u6c8c\u8fb9\u7f18 <\/span>(Pierre and H\u00fcbler, 1994, Baym and H\u00fcbler, 2006, Melby et al., 2000)<\/span>\u3002\u6b64\u5916\uff0c\u591a\u5e74\u6765\uff0c\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u4e5f\u6d3e\u751f\u51fa\u8bb8\u591a\u65b0\u5c5e\u6027\u3002\u4f8b\u5982\uff0c\u5728Kc<\/sub>\u5904\uff0c\u5438\u5f15\u5b50\u5468\u671f\u7684\u76f8\u7a7a\u95f4\u7ed3\u6784<\/span>\uff08Albert and Barab\u00e1si, 2000\uff09<\/span>\uff0c\u4e0d\u540c\u5438\u5f15\u5b50\u7684\u6570\u91cf<\/span>\uff08Samuelsson and Troein, 2003\uff09<\/span>\uff0c\u6df7\u6c8c\u5438\u5f15\u5b50\u7684\u5206\u5e03\u662f\u590d\u6742\u7684<\/span>\uff08Bastolla and Parisi, 1998\uff09<\/span>\uff0c\u663e\u793a\u51fa\u8bb8\u591a\u751f\u7269\u7f51\u7edc\u7684\u5c5e\u6027 <\/span>(Kaukman,1993) <\/span>\u3002<\/span><\/section>\n

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2000\u5e74\uff0cBornholdt \u548c Rohlf<\/span> (2000)<\/span> \u8bc1\u660e\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u5c40\u90e8\u91cd\u8fde\u89c4\u5219<\/span>\uff08\u9759\u8282\u70b9\u589e\u957f\u8fde\u8fb9\uff0c\u52a8\u8282\u70b9\u5931\u53bb\u8fde\u8fb9\uff09<\/span>\u53ef\u4ee5\u9a71\u52a8\u968f\u673a\u9608\u503c\u7f51\u7edc<\/span>\uff08RTNs\uff09<\/span>\u2014\u2014<\/span>\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u7684\u5b50\u96c6\uff0c\u5728\u5927\u578b\u7cfb\u7edf\u7684\u6781\u9650\u4e0b\uff0c\u8fbe\u5230\u4e34\u754c\u5e73\u5747\u8fde\u901a\u6027K<\/span>c<\/sub>=2\u3002\u8be5\u7ed3\u679c\u540e\u6765\u88ab\u63a8\u5e7f\u5230\u968f\u673a\u5e03\u5c14\u7f51\u7edc<\/span>\uff08Rohlf et al., 2007\uff09<\/span>\u3002\u8fd9\u4e2a\u7ed3\u8bba\u9996\u6b21\u8bc1\u660e\u4e86\uff1a\u4e00\u4e2a\u7b80\u5355\u7684\u81ea\u7ec4\u7ec7\u7f51\u7edc\u7684\u5c40\u90e8\u89c4\u5219\u53ef\u4ee5\u5bfc\u81f4\u5b83\u4eec\u8fdb\u5165\u4e34\u754c\u72b6\u6001\u3002Liu \u548c Bassler <\/span>(2006) <\/span>\u4f7f\u7528\u4e86\u76f8\u540c\u7684\u91cd\u8fde\u89c4\u5219\uff0c\u4f46\u5728\u5171\u540c\u8fdb\u5316\u7684\u8fc7\u7a0b\u4e2d\u3002\u4ed6\u4eec\u53d1\u73b0\u201c\u5728\u6f14\u5316\u8fc7\u7a0b\u4e2d\uff0c\u4e34\u754c\u6001\u7684\u6d8c\u73b0\u6e90\u4e8e\u62d3\u6251\u5b66\u548c\u52a8\u529b\u5b66\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u201d<\/span><\/section>\n

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Goudarzi \u7b49\u4eba<\/span> (2012) <\/span>\u66f4\u8fdb\u4e00\u6b65\uff0c\u89e3\u51b3\u4e86\u4e00\u4e2a\u957f\u671f\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\uff1a\u4ed6\u4eec\u901a\u8fc7\u8ba1\u7b97\u53d1\u73b0\uff0c\u5bf9\u4e8e\u5927\u89c4\u6a21<\/span>\uff08N\uff09<\/span>\u7684\u7cfb\u7edf\uff0c\u81ea\u9002\u5e94\u4fe1\u606f\u5904\u7406\u9a71\u4f7f\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u7684\u4e34\u754c\u8fde\u901a\u6027K<\/span>c<\/sub>=2<\/span>\u3002\u5bf9\u4e8e\u6709\u9650\u89c4\u6a21\u7684\u7f51\u7edc\uff0c\u8fde\u901a\u5ea6\u63a5\u8fd1\u4e34\u754c\u503c\uff0c\u4e14\u4e0e\u7cfb\u7edf\u89c4\u6a21\u5448\u5e42\u5f8b\u5173\u7cfb\ud835\udc41\u3002\u6b64\u5916\uff0c\u4ed6\u4eec\u8fd8\u8868\u660e\uff0c\u5982\u679c\u4efb\u52a1\u590d\u6742\u6027\u548c\u6240\u63d0\u4f9b\u7684\u4fe1\u606f\u91cf\u8d85\u8fc7\u4e86\u4e00\u5b9a\u7684\u590d\u6742\u6027\u9608\u503c\uff0c\u7f51\u7edc\u5b66\u4e60\u548c\u6cdb\u5316\u5728\u63a5\u8fd1\u4e34\u754c\u72b6\u6001\u65f6\u4f1a\u5f97\u5230\u4f18\u5316\u3002<\/span><\/section>\n

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\u5927\u7ea6\u662f2001\u5e74\uff0c\u51fa\u73b0\u4e86\u4e00\u79cd\u65b0\u7684\u7814\u7a76\u65b9\u5411\u2014\u2014\u5e93\u8ba1\u7b97Reservoir Computing<\/span> (RC)<\/span>\uff08Jaeger, 2001; Bertschinger and Natschl\u00e4ger, 2004, Maass et al., 2002, Legenstein and Maass, 2007\uff09<\/span>\u3002\u5e93\u8ba1\u7b97\u7684\u4e3b\u8981\u601d\u60f3\u662f\uff1a1\uff09\u4e00\u4e2a\u9012\u5f52\u795e\u7ecf\u7f51\u7edc\u4f5c\u4e3a\u4e00\u4e2a\u56fa\u5b9a\u7684\u3001\u5178\u578b\u5730\u975e\u7ebf\u6027\u7684\u201c\u50a8\u5b58\u5668\uff0c\u201d\u5b83\u5c06\u8f93\u5165\u6295\u5f71\u5230\u4e00\u4e2a\u66f4\u9ad8\u7ef4\u7684\u7a7a\u95f4\uff1b2\uff09\u8bad\u7ec3\u7ebf\u6027\u8f93\u51fa\u5c42\u5c06\u9ad8\u7ef4\u7a7a\u95f4\u6620\u5c04\u5230\u671f\u671b\u7684\u8f93\u51fa\u4e0a\uff0c\u540e\u4e00\u90e8\u5206\u5927\u5927\u964d\u4f4e\u4e86\u8bad\u7ec3\u7684\u8ba1\u7b97\u6210\u672c\u3002\u5e93\u8ba1\u7b97\u5df2\u7ecf\u4ece\u4e00\u4e2a\u8fb9\u7f18\u6982\u5ff5\u53d1\u5c55\u6210\u4e3a\u4e00\u4e2a\u76f8\u5f53\u4e3b\u6d41\u7684\u8ba1\u7b97\u6846\u67b6<\/span>\uff08B\u00fcsing et al., 2010, Goudarzi and Teuscher, 2016\uff09<\/span>\u3002\u5e93\u8ba1\u7b97\u5728\u65f6\u95f4\u4fe1\u53f7\u5904\u7406\u9886\u57df\u5c24\u5176\u51fa\u8272\uff0c\u7136\u800c\uff0c\u89e6\u987b\u5c42\u53ef\u80fd\u662f\u975e\u7ed3\u6784\u5316\u3001\u4e0d\u5b8c\u7f8e\u548c\u4e0d\u53ef\u9760\u7684\uff0c\u8fd9\u4e00\u4e8b\u5b9e\u5f15\u8d77\u4e86\u786c\u4ef6\u754c\u7684\u5173\u6ce8\uff0c\u56e0\u4e3a\u5b83\u6709\u53ef\u80fd\u4f7f\u50a8\u5c42\u7684\u6784\u5efa\u6bd4\u4f20\u7edf\u786c\u4ef6\u66f4\u5bb9\u6613\u3001\u66f4\u4fbf\u5b9c\u3002\u8fd9\u53c8\u5f15\u51fa\u4e86\u53e6\u4e00\u4e2a\u65b0\u9886\u57df\uff1a\u975e\u7269\u8d28\u8ba1\u7b97<\/span>\uff08Lilak et al., 2021, Dale et al., 2017, Hochstetter et al., 2021\uff09<\/span>\u3002\u795e\u7ecf\u5f62\u6001\u8ba1\u7b97\u793e\u533a\u5bf9\u8fd9\u4e00\u9886\u57df\u7279\u522b\u611f\u5174\u8da3\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u5229\u7528\u7269\u7406\u5b66\u6765\u5b9e\u73b0\u795e\u7ecf\u7f51\u7edc\u7684\u6f5c\u529b\uff0c\u800c\u4e0d\u662f\u5efa\u7acb\u4f20\u7edf\u7684\u51af\u00b7\u8bfa\u4f9d\u66fc\u4f53\u7cfb\u7ed3\u6784\u7136\u540e\u201c\u6a21\u62df\u201d\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Nakajima et al., 2021, Hochstetter et al., 2021, Cao et al., 2022, Tran and Teuscher, 2021, Slavova and Ignatov, 2022\uff09<\/span>\u3002<\/span><\/section>\n

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\u5e93\u8ba1\u7b97\u6210\u4e3a\u7814\u7a76\u8005\u7814\u7a76\u6df7\u6c8c\u8fb9\u7f18\u7684\u6700\u65b0\u6e38\u4e50\u573a\u4e4b\u4e00\u3002Boedecker\u7b49\u4eba<\/span>\uff082012\u5e74\uff09<\/span>\u4f7f\u7528\u4e86\u4e00\u4e2a\u4fe1\u606f\u7406\u8bba\u6846\u67b6\uff0c\u8868\u660e\u5f53\u50a8\u84c4\u5c42\u5904\u4e8e\u7a33\u5b9a\u548c\u4e0d\u7a33\u5b9a\u72b6\u6001\u4e4b\u95f4\u65f6\uff0c\u5373\u6df7\u6c8c\u8fb9\u7f18\uff0c\u56de\u58f0\u72b6\u6001\u7f51\u7edc<\/span>\uff08\u5e93\u8ba1\u7b97\u7684\u4e00\u79cd\u53d8\u4f53\uff09<\/span>\u7684\u8ba1\u7b97\u80fd\u529b\u6700\u5927\u3002Snyder\u7b49\u4eba<\/span>\uff082013\u5e74\uff09<\/span>\u6307\u51fa\uff0c\u968f\u673a\u5e03\u5c14\u7f51\u7edc\u5e93\u8ba1\u7b97\u4e2d\u7684\u672c\u5f81\u8ba1\u7b97\u80fd\u529b\uff0c\u5728\u7cfb\u7edf\u5904\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u65f6\u8fbe\u5230\u6700\u5927\u3002Carroll <\/span>\uff082020\uff09<\/span>\u6700\u8fd1\u7684\u7814\u7a76\u4f3c\u4e4e\u4e0e\u65e9\u671f\u5904\u4e8e\u6df7\u6c8c\u8fb9\u7f18\u7684\u5e93\u8ba1\u7b97\u76f8\u5173\u7684\u8bb8\u591a\u7814\u7a76\u76f8\u77db\u76fe\uff1a\u201c\u52a8\u529b\u7cfb\u7edf\u7684\u6700\u4f73\u8ba1\u7b97\u80fd\u529b\u51fa\u73b0\u5728\u7a33\u5b9a\u6027\u8fb9\u7f18\uff0c\u8fd9\u4e00\u6982\u5ff5\uff0c\u901a\u5e38\u662f\u4e0d\u6b63\u786e\u7684\u3002\u672c\u6587\u5c55\u793a\u4e86\u6700\u4f73\u6027\u80fd\u4e0d\u5728\u7a33\u5b9a\u6027\u8fb9\u7f18\u7684\u5e93\u8ba1\u7b97\u3002\u201d Carroll\u5c06\u6df7\u6c8c\u8fb9\u7f18<\/span>\uff08EoC\uff09<\/span>\u91cd\u65b0\u5b9a\u4e49\u4e3a\u7a33\u5b9a\u6027\u8fb9\u7f18<\/span>\uff08EoS\uff09<\/span>\uff0c\u5373\u6700\u5927Lyapunov\u6307\u6570\u53d8\u4e3a\u6b63\u503c\u7684\u70b9\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u4ed6\u7684\u7ed3\u679c\u53ea\u57fa\u4e8e\u5355\u4e00\u4efb\u52a1\u548c\u5355\u4e00\u50a8\u5c42\u5927\u5c0f\u3002\u8fd9\u4e2a\u7ed3\u679c\u662f\u5426\u9002\u7528\u4e8e\u66f4\u666e\u904d\u7684\u60c5\u51b5\u8fd8\u6709\u5f85\u89c2\u5bdf\u3002<\/span><\/section>\n

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\u8bb8\u591a\u590d\u6742\u7cfb\u7edf\uff0c\u5c24\u5176\u662f\u6d3b\u7ec6\u80de\uff0c\u5728\u7ef4\u6301\u5176\u65f6\u7a7a\u7ec4\u7ec7\u65b9\u9762\u8868\u73b0\u51fa\u975e\u51e1\u7684\u7a33\u5b9a\u6027\uff0c\u4f46\u540c\u65f6\uff0c\u5b83\u4eec\u4e5f\u80fd\u591f\u9002\u5e94\u73af\u5883\u4e2d\u7684\u5404\u79cd\u53d8\u5316\u3002\u4e00\u4e2a\u751f\u547d\u7684\u6c42\u751f\u672c\u80fd\u8981\u6c42\u5b83\u80fd\u6574\u5408\u548c\u5904\u7406\u6709\u9650\u7684\u8d44\u6e90\uff0c\u5e76\u5bf9\u73af\u5883\u7684\u53d8\u5316\u4f5c\u51fa\u53cd\u5e94\u3002\u56e0\u6b64\uff0c\u7cfb\u7edf\u5fc5\u987b\u5904\u7406\u5982\u6709\u9650\u7684\u80fd\u91cf\u3001\u8d44\u6e90\u3001\u7a7a\u95f4\u3001\u65f6\u95f4\u7b49\u7684\u53cd\u9988\u548c\u5e73\u8861\uff0c\u624d\u80fd\u6d3b\u4e0b\u53bb\u3002\u5b83\u4eec\u5927\u81f4\u7b26\u5408Liberman \u548c Minina <\/span>(1996) <\/span>\u63d0\u51fa\u7684\u56db\u4e2a\u7edf\u4e00\u7684\u751f\u7269\u57fa\u672c\u539f\u5219\u3002\u4e5f\u6709\u4eba\u5047\u8bbe\uff0c\u751f\u547d\u7cfb\u7edf\u8fdb\u5316\u8fdb\u7a0b\u4e2d\u88ab\u81ea\u7136\u9009\u62e9\u7684\u4f9d\u636e\u662f\u5728\u6df7\u6c8c\u8fb9\u7f18\u9644\u8fd1\u6267\u884c\u590d\u6742\u4fe1\u606f\u5904\u7406\u7684\u80fd\u529b\u3002\u6709\u4eba\u63d0\u51fa\u5e76\u7814\u7a76\u4e86\u51e0\u79cd\u673a\u5236\uff0c\u5b83\u4eec\u5c06\u751f\u547d\u7cfb\u7edf\u4ee5\u53ca\u62bd\u8c61\u7684\u975e\u751f\u547d\u7cfb\u7edf<\/span>\uff08\u5982RBN\uff09<\/span>\u9a71\u52a8\u5230\u4e34\u754c\u72b6\u6001\u3002\u8fd9\u6837\u7684\u81ea\u7ec4\u7ec7\u6709\u591a\u5c11\u662f\u76ee\u6807\u5bfc\u5411\u7684\uff0c\u6709\u591a\u5c11\u4e0d\u662f\uff1f\u4ecd\u662f\u4e00\u4e2a\u60ac\u800c\u672a\u51b3\u7684\u95ee\u9898\u3002<\/span><\/section>\n

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Liberman\u5f00\u521b\u548c\u53d1\u5c55\u7684\u4e00\u4e2a\u6982\u5ff5\uff1a\u7ec6\u80de\u662f\u5206\u5b50\u8ba1\u7b97\u673a\u2014\u2014\u901a\u5e38\u88ab\u89c6\u4e3a\u751f\u547d\u7cfb\u7edf\u5982\u4f55\u7ec4\u7ec7\u548c\u8fd0\u884c\u7684\u6a21\u578b<\/span>\uff08Liberman\uff0c1972\uff09<\/span>\u3002\u8fd9\u79cd\u89c2\u70b9\u4e0b\uff0c\u8ba1\u7b97\u673a\u88ab\u89c6\u4f5c\u5904\u4e8e\u4e34\u754c\u72b6\u6001\u7684\u7269\u7406\u7cfb\u7edf\u3002\u5b83\u4eec\u8981\u5728\u4e00\u5b9a\u7684\u5b8f\u89c2\u201c\u8ba1\u7b97\u201d\u81ea\u7531\u5ea6\u5185\u652f\u6301\u4efb\u610f\u957f\u7684\u65f6\u95f4\u76f8\u5173\u6027\u3002\u8fd9\u901a\u8fc7\u5c06\u8fd9\u4e9b\u81ea\u7531\u5ea6\u4e0e\u4ea7\u751f\u8bef\u5dee\u7684\u70ed\u6d74\u81ea\u7531\u5ea6\u89e3\u8026\u6765\u5b9e\u73b0\u3002\u8ba1\u7b97\u673a\u662f\u4e00\u79cd\u7269\u7406\u7cfb\u7edf\uff0c\u5728\u71b5\u65e0\u5e8f\u73af\u5883\u4e2d\u5904\u4e8e\u8fde\u7eed\u76f8\u53d8\u72b6\u6001\u3002\u5728\u8fd9\u6837\u7684\u73af\u5883\u91cc\uff0c\u8ba1\u7b97\u673a\u83b7\u5f97\u4e86\u63a8\u52a8\u8ba1\u7b97\u5411\u524d\u53d1\u5c55\u7684\u9a71\u52a8\u529b\u3002\u4f46\u540c\u65f6\uff0c\u5b83\u4eec\u5fc5\u987b\u4fdd\u62a4\u8ba1\u7b97\u4e0d\u53d7\u73af\u5883\u5f15\u8d77\u7684\u6ce2\u52a8\u7684\u5f71\u54cd<\/span>\uff08Crutchfield and Young, 1990\uff09<\/span>\u3002<\/span><\/section>\n

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\u603b\u7ed3\u5982\u4e0b\uff1a\u6839\u636eBetteridge\u5b9a\u5f8b\u548cHinchcliffe\u89c4\u5219<\/span>\uff08Cook and Plourde\uff0c2016\uff09<\/span>\uff0c\u5f53\u6587\u7ae0\u6807\u9898\u63d0\u51fa\u662f\u6216\u5426\u7684\u95ee\u9898\u65f6\uff0c\u95ee\u9898\u7684\u7b54\u6848\u901a\u5e38\u662f\u5426\u5b9a\u7684\u3002\u76ee\u524d\u4f3c\u4e4e\u4e5f\u6ca1\u6709\u5fc5\u8981\u91cd\u5bfb\u6df7\u6c8c\u8fb9\u7f18\u3002\u6211\u4eec\u53ef\u4ee5\u5f88\u6709\u4fe1\u5fc3\u5730\u8bf4\uff0c\u8fd9\u4e00\u6982\u5ff5\u5df2\u7ecf\u786e\u7acb\uff0c\u4e14\u5728\u5404\u4e2a\u9886\u57df\uff0c\u4ee5\u5404\u79cd\u65b9\u6cd5\u5f97\u5230\u4e86\u8bc1\u660e\u3002<\/span><\/section>\n

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