{"id":38611,"date":"2022-11-20T21:08:58","date_gmt":"2022-11-20T13:08:58","guid":{"rendered":"https:\/\/swarma.org\/?p=38611"},"modified":"2022-11-20T21:08:58","modified_gmt":"2022-11-20T13:08:58","slug":"%e6%b7%b7%e6%b2%8c%e7%a7%91%e5%ad%a6%e7%b3%bb%e5%88%97%e7%a7%91%e6%99%ae%e8%af%be%e7%a8%8b%ef%bc%9a%e7%a1%ae%e5%ae%9a%e6%80%a7%e7%9a%84%e7%b3%bb%e7%bb%9f%e6%97%a0%e6%b3%95%e9%a2%84%e6%b5%8b%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=38611","title":{"rendered":"\u6df7\u6c8c\u79d1\u5b66\u7cfb\u5217\u79d1\u666e\u8bfe\u7a0b\uff1a\u786e\u5b9a\u6027\u7684\u7cfb\u7edf\u65e0\u6cd5\u9884\u6d4b\uff1f"},"content":{"rendered":"
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21\u4e16\u7eaa\u662f\u590d\u6742\u6027\u7684\u4e16\u7eaa\uff0c\u7406\u89e3\u6df7\u6c8c\u662f\u63a2\u7d22\u590d\u6742\u6027\u7684\u5173\u952e\u73af\u8282\u3002\u5728\u79d1\u5b66\u3001\u5de5\u7a0b\u4e2d\uff0c\u6df7\u6c8c\u4e0e\u975e\u7ebf\u6027\u65b9\u6cd5\u5df2\u7ecf\u6210\u4e3a\u7814\u7a76\u52a8\u6001\u7cfb\u7edf\u7684\u4e3b\u8981\u624b\u6bb5\uff0c\u52a0\u6df1\u4e86\u5bf9\u6c14\u5019\u3001\u751f\u6001\u3001\u5927\u8111\u3001\u6d41\u884c\u75c5\u7b49\u8bf8\u591a\u590d\u6742\u7cfb\u7edf\u95ee\u9898\u7684\u7406\u89e3\uff0c\u5e76\u5728\u6e4d\u6d41\u3001\u52a0\u5bc6\u3001\u6570\u636e\u5206\u6790\u4ee5\u53ca\u751f\u547d\u79d1\u5b66\u4e2d\u6709\u5e7f\u6cdb\u5e94\u7528\u3002\u5728\u793e\u4f1a\u3001\u5546\u4e1a\u9886\u57df\uff0c\u6df7\u6c8c\u7406\u8bba\u5728\u901a\u8baf\u3001\u4ea4\u901a\u3001\u91d1\u878d\u5e02\u573a\u3001\u75be\u75c5\u4e0e\u4fe1\u606f\u4f20\u64ad\u7b49\u95ee\u9898\u4e2d\u4ea6\u6709\u8bf8\u591a\u542f\u53d1\u548c\u5e94\u7528\u3002\u968f\u7740\u6df7\u6c8c\u73b0\u8c61\u7684\u8fdb\u4e00\u6b65\u7cfb\u7edf\u7814\u7a76\u548c\u5e7f\u6cdb\u5e94\u7528\uff0c\u5b83\u6b63\u5728\u4ece\u4e00\u5957\u7406\u8bba\u53d1\u5c55\u4e3a\u4e00\u95e8\u79d1\u5b66\u3002<\/span><\/strong><\/p>\n


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\u90a3\u4e48\uff0c\u5bf9\u5929\u6c14 100% \u7684\u7cbe\u786e\u9884\u6d4b\uff0c\u662f\u5426\u5e94\u8be5\u6210\u4e3a\u4e00\u4e2a\u6c14\u8c61\u5b66\u5bb6\u7684\u8ffd\u6c42\u5462\uff1f\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u6211\u4eec\u5bf9\u7cfb\u7edf\u7684\u8fd0\u884c\u539f\u7406\u6709\u6df1\u523b\u7684\u6d1e\u5bdf\u3002\u800c\u7b54\u6848\u662f\u5426\u5b9a\u7684\u3002\u5373\u4fbf\u6570\u636e\u518d\u7cbe\u786e\uff0c\u6280\u672f\u518d\u8fdb\u6b65\uff0c\u786e\u5b9a\u6027\u6df7\u6c8c\u7406\u8bba\u8868\u660e\u5b83\u4eec\u7684\u9884\u6d4b\u6c38\u8fdc\u4e0d\u4f1a\u7cbe\u786e\u3002\u6211\u4eec\u627f\u8ba4\u8fd9\u662f\u4e00\u95e8\u4e0d\u5b8c\u7f8e\u7684\u79d1\u5b66<\/strong>\uff0c\u5b83\u63d0\u4f9b\u7684\u662f\u9884\u6d4b\u7ed3\u679c\u7684\u6982\u7387\u3002\u6df7\u6c8c\u5f00\u59cb\u7684\u5730\u65b9\uff0c\u7ecf\u5178\u79d1\u5b66\u5931\u6548\uff0c\u51b3\u5b9a\u8bba\u5f0f\u7684\u53ef\u9884\u6d4b\u6027\u7684\u62c9\u666e\u62c9\u65af\u5f0f\u7684\u5e7b\u60f3\u7834\u706d\u3002<\/span><\/section>\n
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\u6d1b\u4f26\u5179\uff08Lorenz\uff09\uff0c\u4e00\u4f4d\u7814\u7a76\u5927\u6c14\u7269\u7406\u7684\u6c14\u8c61\u5b66\u5bb6\uff0c\u5bf9\u6df7\u6c8c\u73b0\u8c61\u7684\u7814\u7a76\u4ee5\u53ca\u6df7\u6c8c\u7406\u8bba\u7684\u63d0\u51fa\u505a\u51fa\u4e86\u91cd\u8981\u7684\u8d21\u732e\u3002\u4ed6\u7528\u4e00\u4e2a\u7b80\u5355\u5177\u4f53\u7684\u7269\u7406\u5b66\u6a21\u578b\u53ca\u5176\u6570\u5b66\u539f\u7406\u5411\u4e16\u4eba\u793a\u660e\uff1a\u7cbe\u786e\u7684\u957f\u671f\u5929\u6c14\u9884\u62a5\u7684\u786e\u662f\u4e0d\u53ef\u80fd\u7684\u3002<\/span><\/section>\n

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A chaotic system is one where extraordinarily slight changes in initial conditions (blue and yellow)<\/span><\/p>\n

HELLISP OF WIKIMEDIA COMMONS \/ CREATED BY XAOSBITS USING MATHEMATICA AND POV-RAY<\/span><\/p>\n


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\u5728 1961 \u5e74\uff0c\u4ed6\u5efa\u7acb\u4e86\u4e00\u4e2a\u4e09\u7ef4\u4e8c\u6b21\u591a\u9879\u5f0f\u5fae\u5206\u65b9\u7a0b\u5929\u6c14\u9884\u62a5\u6a21\u578b\u3002\u501f\u52a9\u8ba1\u7b97\u673a\uff0c\u4ed6\u8f93\u5165\u5f53\u524d\u5929\u6c14\u7684\u72b6\u51b5\u53bb\u8fed\u4ee3\u9884\u6d4b\u672a\u6765\u7684\u5929\u6c14\u3002\u5728\u4e00\u6b21\u91cd\u590d\u5b9e\u9a8c\u4e2d\uff0c\u4ed6\u628a\u4e4b\u524d\u6570\u636e\u76f4\u63a5\u8f93\u5165\u8ba1\u7b97\u673a\u2014\u2014\u540c\u6837\u7684\u6570\u636e\uff0c\u540c\u6837\u7684\u7b97\u6cd5\uff0c\u7406\u5e94\u5f97\u5230\u76f8\u540c\u7684\u7ed3\u679c\u3002\u4f46\u662f\u9884\u6d4b\u7ed3\u679c\u968f\u7740\u65f6\u95f4\u8d8a\u957f\uff0c\u5dee\u8ddd\u8d8a\u5927\u3002\u4ed6\u4ed4\u7ec6\u68c0\u67e5\u540e\uff0c\u53d1\u73b0\u5728\u8f93\u5165\u6570\u636e\u65f6\uff0c\u5c06\u539f\u6765\u7684\u6570\u5b57\u201c0.506127\u201d\uff0c\u7b80\u5316\u4e3a\u201c0.506\u201d\u8f93\u5165\u8ba1\u7b97\u3002\u4e0d\u5230\u5343\u5206\u4e4b\u4e00\u7684\u5dee\u8ddd\uff0c\u5bfc\u81f4\u8ba1\u7b97\u7ed3\u679c\u51fa\u73b0\u4e86\u6781\u5927\u7684\u5dee\u5f02\uff0c\u8fd9\u5f15\u53d1\u4e86\u4ed6\u7684\u6ce8\u610f<\/strong>\u3002\u521d\u59cb\u6761\u4ef6\u7684\u5fae\u5c0f\u5dee\u5f02\uff0c\u7adf\u4ea7\u751f\u5982\u6b64\u60ca\u4eba\u7684\u5dee\u5f02\u3002<\/span><\/section>\n

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1963 \u5e74\u6d1b\u4f26\u5179\u7684\u8bba\u6587\u300aDeterministic Nonperiodic Flow\u300b\u53d1\u8868\u540e\uff0c\u4eba\u4eec\u5f00\u59cb\u4e86\u5bf9\u8fd9\u7c7b\u73b0\u8c61\u7684\u6df1\u5165\u7814\u7a76\u3002\u540e\u6765\uff0c\u6d1b\u4f26\u5179\u7684\u7814\u7a76\u7a81\u7834\u4e86\u5929\u6c14\u7814\u7a76\u9886\u57df\u7684\u9650\u5236\uff0c\u6210\u4e3a\u4e00\u4e2a\u53d7\u5230\u5168\u4e16\u754c\u79d1\u5b66\u5bb6\u5173\u6ce8\u7684\u8de8\u8d8a\u4f20\u7edf\u5b66\u79d1\u7684\u65b0\u9886\u57df\u30021975\u5e74\uff0c\u674e\u5929\u5ca9\u548cJames Yorke \u6b63\u5f0f\u5c06\u5176\u547d\u540d\u4e3a\u201c\u6df7\u6c8c\u7406\u8bba\u201d\u3002\u4e00\u95e8\u65b0\u79d1\u5b66\u4ece\u6b64\u8bde\u751f\u3002<\/span><\/section>\n

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\u6df7\u6c8c\u79d1\u5b66\u5f00\u542f\u4e86\u4e00\u79cd\u7406\u89e3\u4e16\u754c\u8fd0\u884c\u65b9\u5f0f\u7684\u65b0\u601d\u60f3\u3002\u7c97\u7565\u5730\u8bf4\uff0c\u201c\u6df7\u6c8c\u201d\u662f\u5f88\u591a\u81ea\u7136\u548c\u793e\u4f1a\u7cfb\u7edf\u7684\u4e00\u79cd\u7279\u522b\u7684\u5f62\u6001\uff0c\u5b83\u6700\u57fa\u672c\u7684\u7279\u6027\u662f\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u9ad8\u5ea6\u654f\u611f\u6027\uff0c\u5373\u201c\u8774\u8776\u6548\u5e94\u201d\u3002<\/strong>\u6b64\u5916\uff0c\u5b83\u8868\u73b0\u4e3a\u5c40\u90e8\u6d3b\u8dc3\uff08\u4e0d\u6536\u655b\uff09\u3001\u5168\u57df\u6709\u754c\uff08\u4e0d\u53d1\u6563\uff09\u3001\u975e\u4e25\u683c\u5468\u671f\uff08\u65e0\u7a77\u591a\u4e2a\u5468\u671f\u7ec4\u5206\u7684\u590d\u5408\uff09\u7684\u8fd0\u52a8\u72b6\u6001\u3002\u5177\u4f53\u4e00\u70b9\u6765\u8bf4\uff0c\u6df7\u6c8c\u7cfb\u7edf\u662f\u5c40\u90e8\u4e0d\u7a33\u5b9a\u7684\uff0c\u5373\u4e0d\u4f1a\u6536\u655b\u5230\u4e00\u4e2a\u5730\u65b9\u7136\u540e\u5c31\u4e0d\u52a8\u4e86\uff1b\u5b83\u53c8\u662f\u5168\u57df\u7a33\u5b9a\u7684\uff0c\u5373\u4e0d\u4f1a\u53d1\u6563\u5230\u65e0\u7a77\u8fdc\u5904\u800c\u6d88\u5931\u4e86\uff1b\u5b83\u8fd8\u5728\u8fd1\u4e4e\u5468\u671f\u5374\u4e0d\u662f\u4e25\u683c\u5468\u671f\u5730\u53d8\u5316\uff0c\u8bf8\u5982\u4e00\u5e74\u56db\u5b63\u5468\u800c\u590d\u59cb\uff0c\u4f46\u6bcf\u5e74\u90fd\u4f1a\u6709\u4e00\u4e9b\u5dee\u5f02\u3002\u6df7\u6c8c\u5f62\u6001\u7684\u672c\u8d28\u662f\u786e\u5b9a\u6027\u7684\uff0c\u4f46\u7531\u4e8e\u7cfb\u7edf\u5185\u7684\u975e\u7ebf\u6027\u76f8\u4e92\u4f5c\u7528\uff0c\u4ea7\u751f\u4e86\u770b\u4f3c\u968f\u673a\u6027\u7684\u884c\u4e3a\u3002<\/strong><\/span><\/section>\n

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\u79d1\u5b66\u7684\u4efb\u52a1\u662f\u89e3\u91ca\u81ea\u7136\u4e16\u754c\uff0c\u6280\u672f\u7684\u76ee\u6807\u624d\u662f\u4e3a\u4eba\u7c7b\u793e\u4f1a\u670d\u52a1\u3002\u6df7\u6c8c\u79d1\u5b66\u89e3\u91ca\u4e86\u81ea\u7136\u754c\u548c\u4eba\u7c7b\u793e\u4f1a\u4e2d\u7684\u67d0\u4e9b\u5185\u5bb9\u89c4\u5f8b\uff0c\u8ba9\u6211\u4eec\u66f4\u52a0\u660e\u767d\u81ea\u8eab\u4e4b\u5916\u7684\u4e8b\u7269\u53d1\u5c55\uff0c\u8fdb\u800c\u5e2e\u52a9\u6211\u4eec\u53bb\u53d1\u5c55\u73b0\u4eca\u6280\u672f\uff0c\u4ee5\u6539\u826f\u4e16\u754c\u4e3a\u4eba\u7c7b\u670d\u52a1\u3002\u548c\u5176\u4ed6\u5b66\u79d1\u4e00\u6837\uff0c\u6df7\u6c8c\u7406\u8bba\u5728\u6f14\u8fdb\u7684\u8fc7\u7a0b\u4e2d\u4e5f\u9010\u6b65\u88ab\u5229\u7528\u6765\u53d1\u5c55\u4e00\u4e9b\u6709\u7528\u7684\u6280\u672f\u3002\u5728\u8111\u79d1\u5b66\u3001\u52a0\u5bc6\u901a\u4fe1\u3001\u673a\u68b0\u632f\u52a8\u3001\u7535\u5b50\u8bbe\u5907\u3001\u751f\u7269\u533b\u836f\u3001\u751f\u6001\u5efa\u6a21\u3001\u6c14\u8c61\u9884\u6d4b\u3001\u6d41\u4f53\u529b\u5b66\u3001\u975e\u7ebf\u6027\u7269\u7406\u7b49\u6709\u5e7f\u6cdb\u5e94\u7528\u3002<\/span><\/section>\n

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\u52a8\u529b\u5b66\u5206\u6790\u662f\u7814\u7a76\u590d\u6742\u7cfb\u7edf\u7684\u4e00\u79cd\u91cd\u8981\u624b\u6bb5\u3002\u6df7\u6c8c\u662f\u5176\u4e2d\u91cd\u8981\u7684\u7ec4\u6210\u90e8\u5206\uff0c\u53ef\u4ee5\u5e2e\u6211\u4eec\u66f4\u597d\u5730\u7814\u7a76\u7cfb\u7edf\u7684\u6f14\u5316\u89c4\u5f8b\uff0c\u52a0\u4ee5\u9884\u6d4b\u3001\u63a7\u5236\u4e0e\u5229\u7528\u3002<\/span><\/section>\n

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\u4e3a\u4e86\u5411\u8de8\u5b66\u79d1\u5b66\u4e60\u8005\u666e\u53ca\u6df7\u6c8c\u79d1\u5b66\u7684\u7406\u8bba\u672c\u8d28\uff0c\u4ece\u800c\u80fd\u5e94\u7528\u5728\u81ea\u5df1\u7684\u7814\u7a76\u3001\u63a2\u7d22\u4e2d\uff0c\u5e2e\u52a9\u5927\u5bb6\u5206\u6790\u3001\u7406\u89e3\u3001\u8ba4\u77e5\u5176\u4e2d\u7684\u590d\u6742\u6027\u3002\u96c6\u667a\u5b66\u56ed\u8054\u5408\u9648\u5173\u8363\u3001\u738b\u96c4\u3001\u674e\u6625\u5f6a\u3001\u5f20\u65ed\u3001\u9a6c\u519b\u3001\u5218\u575a\u3001\u738b\u9752\u4e91\u3001\u53f6\u56fd\u680b\u3001\u79b9\u601d\u654f\u4e5d\u4f4d\u56fd\u5185\u7684\u6df7\u6c8c\u7406\u8bba\u7814\u7a76\u4e13\u5bb6\uff0c\u53d1\u8d77\u4e86\u201c\u6df7\u6c8c\u79d1\u5b66\u201d\u7cfb\u5217\u79d1\u666e\u8bfe\u7a0b\u3002<\/span><\/section>\n

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\u8bfe\u7a0b\u6846\u67b6\u7684\u4ecb\u7ecd<\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u5168\u8bfe\u7a0b\u51719\u8282\u6838\u5fc3\u8bfe\u7a0b+2-3\u8282\u5b9e\u8df5\u8bfe\u7a0b\u3002<\/strong><\/span><\/p>\n

\u5bfc\u5f15\u6a21\u5757\uff1a<\/strong>\u7b2c 1 \u8282\uff0c\u4ee5\u8bb2\u8ff0\u5386\u53f2\u548c\u4eba\u7269\u6545\u4e8b\u7684\u5f62\u5f0f\u6765\u4ecb\u7ecd\u6df7\u6c8c\u79d1\u5b66\u7684\u5f62\u6210\u548c\u53d1\u5c55\u4ee5\u53ca\u4e00\u4e9b\u76f8\u5173\u6982\u5ff5\u548c\u7406\u8bba\uff0c\u4f5c\u4e3a\u7cfb\u5217\u8bfe\u7a0b\u7684\u5bfc\u5f15\u3002<\/span><\/p>\n

\u57fa\u7840\u7406\u8bba\u6a21\u5757\uff1a<\/strong><\/span>\u7b2c 2-6 \u8282\uff0c\u4ece\u6d1b\u4f26\u5179<\/span>\u7cfb\u7edf\u5230\u5176\u4ed6\u6df7\u6c8c\u7cfb\u7edf\uff0c\u6df7\u6c8c\u4fe1\u53f7\u8c03\u63a7\u53ca\u6df7\u6c8c\u5fc6\u963b\u5668\u5efa\u6a21\uff0cSmale\u9a6c\u8e44\u7684\u6784\u9020\u3001\u5206\u6790\u4e0e\u5e94\u7528\uff0c\u65f6\u7a7a\u7cfb\u7edf\u6591\u56fe\uff0c\u590d\u6df7\u6c8c\u7cfb\u7edf\u53ca\u5206\u5f62\u7406\u8bba\u7b49\u3002<\/span><\/p>\n

\u5e94\u7528\u6a21\u5757<\/span><\/strong>\uff1a\u7b2c 7-8 \u8282\uff0c\u4ecb\u7ecd\u6df7\u6c8c\u7cfb\u7edf\u5728\u795e\u7ecf\u79d1\u5b66\u53ca\u52a0\u5bc6\u9886\u57df\u7684\u5e94\u7528\u3002<\/span><\/p>\n

\u5b9e\u8df5\u6a21\u5757<\/span><\/strong>\uff1a\u7b2c 9 \u8282\uff0c\u4e0e\u7535\u8def\u8bbe\u8ba1\u7684\u914d\u5408\u662f\u6df7\u6c8c\u7406\u8bba\u843d\u5730\u7684\u91cd\u8981\u57fa\u7840\uff0c\u672c\u8282\u4ecb\u7ecd\u6df7\u6c8c\u7535\u8def\u8bbe\u8ba1\u7684\u76f8\u5173\u77e5\u8bc6\u3002<\/span><\/p>\n

\u5b9e\u8df5\u8bfe\u7a0b\u6839\u636e\u5177\u4f53\u60c5\u51b5\u5b89\u6392\u3002<\/strong><\/p>\n


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\u5bfc\u5f15\u6a21\u5757<\/strong><\/span><\/section>\n
\u7b2c 1 \u8282<\/strong>\uff0c\u4ee5\u8bb2\u8ff0\u5386\u53f2\u548c\u4eba\u7269\u6545\u4e8b\u7684\u5f62\u5f0f\u6765\u4ecb\u7ecd\u6df7\u6c8c\u79d1\u5b66\u7684\u5f62\u6210\u548c\u53d1\u5c55\u4ee5\u53ca\u4e00\u4e9b\u76f8\u5173\u6982\u5ff5\u548c\u7406\u8bba<\/strong>\uff0c\u4f5c\u4e3a\u7cfb\u5217\u79d1\u666e\u8bfe\u7a0b\u7684\u5bfc\u5f15\u3002<\/span><\/section>\n

<\/section>\n
\u57fa\u7840\u7406\u8bba\u6a21\u5757<\/strong><\/span><\/section>\n
\u7b2c 2 \u8282<\/strong>\uff0c<\/span>\u5c06\u7531\u6d45\u5165\u6df1\u7cfb\u7edf\u4ecb\u7ecd\u8fde\u7eed\u7cfb\u7edf\u6df7\u6c8c\u7684\u5404\u79cd\u4f8b\u5b50\u53ca\u57fa\u672c\u6982\u5ff5\u548c\u7406\u8bba\u524d\u6cbf\u52a8\u6001<\/strong>\u3002<\/span><\/section>\n
\u7b2c 3 \u8282<\/span><\/strong>\uff0c\u4ece\u6df7\u6c8c\u4fe1\u53f7\u7684\u8c03\u5e45\u3001\u8c03\u9891\u548c\u8c03\u504f\u7f6e\u51fa\u53d1<\/strong>\uff0c\u7cfb\u7edf\u4ecb\u7ecd\u4e00\u7cfb\u5217\u5177\u6709\u72ec\u7acb\u975e\u5206\u5c94\u53c2\u6570\u7684\u6df7\u6c8c\u52a8\u529b\u5b66\u7cfb\u7edf\uff0c\u901a\u8fc7\u7cfb\u7edf\u53c2\u6570\u7684\u8c03\u6574\u5b9e\u73b0\u7cfb\u7edf\u8f93\u51fa\u6df7\u6c8c\u4fe1\u53f7\u7684\u8c03\u63a7\u3002<\/span>\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u4e5f<\/span>\u7ed3\u5408\u7b2c\u56db\u79cd\u7535\u8def\u5143\u4ef6\u5fc6\u963b\u5668\u7684\u5efa\u6a21\uff0c\u91cd\u65b0\u8bbe\u8ba1\u6df7\u6c8c\u7cfb\u7edf<\/strong>\uff0c\u5b9e\u73b0\u57fa\u4e8e\u5fc6\u963b\u5668\u7684\u6df7\u6c8c\u4fe1\u53f7\u7684\u5168\u9762\u8c03\u7406\u3002<\/span><\/section>\n
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\u7b2c 4 \u8282<\/strong>\uff0c\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\u9a6c\u8e44\u7684\u53d1\u73b0\uff0c\u9a6c\u8e44\u7684\u6784\u9020\uff0c\u52a8\u529b\u5b66\u884c\u4e3a\u7b26\u53f7\u63cf\u8ff0<\/strong>\uff0c\u4e00\u4e9b\u5177\u4f53\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u9a6c\u8e44\u7684\u5206\u6790\u548c\u5e94\u7528\u3002<\/span><\/section>\n
\u7b2c 5 \u8282\uff0c<\/strong>\u5c06\u4ece\u8026\u5408\u632f\u5b50\u7f51\u7edc\u3001\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u540c\u6b65\u7a33\u5b9a\u6027\u3001\u6591\u56fe\u5f62\u6210\u548c\u884c\u6ce2\u4f20\u64ad\u7b49\u65b9\u9762\u5c55\u5f00\u4ecb\u7ecd<\/strong>\u3002\u91cd\u70b9\u4ecb\u7ecd\u632f\u5b50\u7f51\u7edc\u4e2d\u5c40\u57df\u52a8\u529b\u5b66\u8868\u8fbe\u3001\u80fd\u91cf\u8ba1\u7b97\u3001\u8026\u5408\u901a\u9053\u53ef\u63a7\u6027\u3001\u540c\u6b65\u8868\u5f81\u3001\u5f02\u8d28\u6027\u548c\u7f3a\u9677\u5f62\u6210\u3001\u6591\u56fe\u5f62\u6210\u548c\u65f6\u7a7a\u6df7\u6c8c\u63a7\u5236\u3001\u4ee5\u53ca\u53cd\u5e94\u6269\u6563\u7cfb\u7edf\u8868\u8fbe\u7684\u5fc3\u808c\u7ec4\u7ec7\u4e2d\u87ba\u65cb\u6ce2\u7684\u7269\u7406\u6548\u5e94\u7b49\u3002<\/span><\/section>\n
\u7b2c 6 \u8282<\/strong>\uff0c\u5c06\u4ecb\u7ecd\u51e0\u79cd\u590d\u53d8\u91cf\u6df7\u6c8c\u7cfb\u7edf\u53ca\u540c\u6b65\u63a7\u5236<\/strong>\uff0c\u5c06\u7279\u522b\u8be6\u7ec6\u5730\u8bb2\u89e3\u590d\u6d1b\u4f26\u5179<\/span>\u7cfb\u7edf\u3002\u5e76\u5f15\u5165\u5206\u5f62\u7406\u8bba\uff0c\u4ee5\u590d\u53d8\u51fd\u6570\u7684\u8fed\u4ee3\u5165\u624b\uff0c\u4ecb\u7ecd\u5206\u5f62\u7406\u8bba<\/strong>\u4e2d\u7684Mandelbrot\u96c6\u548cJulia \u96c6\u7b49\u91cd\u8981\u6a21\u578b\u53ca\u5176\u63a7\u5236\u3002\u4ecb\u7ecd\u590d\u6df7\u6c8c\u7cfb\u7edf\u53ca\u5206\u5f62\u6d89\u53ca\u7684\u4e3b\u8981\u7ed3\u679c\u4ee5\u53ca\u6700\u8fd1\u7684\u4e00\u4e9b\u8fdb\u5c55\u3002<\/span><\/section>\n

<\/section>\n
\u5e94\u7528\u6a21\u5757<\/strong><\/span><\/section>\n
\u7b2c 7 \u8282<\/strong>\uff0c\u4e3b\u8981\u5185\u5bb9\u5305\u62ec\u795e\u7ecf\u7cfb\u7edf\u4e2d\u7684\u5b9e\u9a8c\u53d1\u73b0\u53ca\u7ecf\u5178\u6a21\u578b\u7684\u63d0\u51fa\u3001\u795e\u7ecf\u7cfb\u7edf\u4e2d\u6df7\u6c8c\u51fa\u73b0\u7684\u673a\u5236\u53ca\u610f\u4e49\u3001\u5206\u5c94\u5206\u6790\u5728\u795e\u7ecf\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u53ca\u610f\u4e49<\/strong>\u3002<\/span><\/section>\n
\u7b2c 8 \u8282<\/strong>\uff0c\u4e3b\u8981\u4ecb\u7ecd\u6df7\u6c8c\u7cfb\u7edf\uff08\u6620\u5c04\uff09\u7684\u7b80\u8981\u53d1\u5c55\u548c\u51e0\u79cd\u5e38\u89c1\u6df7\u6c8c\u6a21\u578b\uff0c\u63cf\u8ff0\u6df7\u6c8c\u7cfb\u7edf\uff08\u6620\u5c04\uff09\u5728\u56fe\u50cf\u52a0\u5bc6\u4e2d\u7684\u5e94\u7528\u3002\u7279\u522b\u5730\uff0c\u5c06\u4e3b\u8981\u56de\u987e\u57fa\u4e8e\u6df7\u6c8c\u52a0\u5bc6\u7814\u7a76\u7684\u53d1\u5c55\u60c5\u51b5\uff0c\u5e76\u4ecb\u7ecd\u4e24\u7c7b\u4e3b\u8981\u7684\u56fe\u50cf\u9690\u79c1\u4fdd\u62a4\u65b9\u6848\uff0c\u76f4\u63a5\u56fe\u50cf\u52a0\u5bc6\u65b9\u6cd5\u4ee5\u53ca\u53ef\u9006\u56fe\u50cf\u9690\u85cf\u65b9\u6cd5<\/strong>\u3002<\/span><\/section>\n

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\u5b9e\u8df5\u6a21\u5757<\/strong><\/span><\/section>\n
\u7b2c 9 \u8282<\/strong>\uff0c\u5c06\u4ee5\u79d1\u666e\u5316\u3001\u5927\u4f17\u5316\u7684\u65b9\u5f0f\u8bb2\u89e3\u6df7\u6c8c\u7535\u8def\u8bbe\u8ba1\u6240\u9700\u7684\u4e00\u4e9b\u57fa\u7840\u77e5\u8bc6\u3001\u7535\u8def\u8bbe\u8ba1\u4e0e\u4eff\u771f\u3001\u7535\u8def\u5b9e\u9a8c\u4e2d\u7684\u82e5\u5e72\u95ee\u9898<\/strong>\u3002<\/span><\/section>\n

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      <\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n

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      \u9648\u5173\u8363<\/strong><\/span><\/section>\n
      <\/section>\n
      \u4e2a\u4eba\u7b80\u4ecb\uff1a\u9648\u5173\u8363\u6559\u6388<\/strong>1981\u5e74\u83b7\u5e7f\u5dde\u4e2d\u5c71\u5927\u5b66\u8ba1\u7b97\u6570\u5b66\u7855\u58eb\u5b66\u4f4d\uff0c1987\u5e74\u83b7\u7f8e\u56fdTexas A&M \u5927\u5b66\u5e94\u7528\u6570\u5b66\u535a\u58eb\u5b66\u4f4d\uff0c\u5176\u540e\u5728\u7f8e\u56fdRice\u548cHouston\u5927\u5b66\u4efb\u6559\u3002\u81ea2000\u5e74\u8d77\uff0c\u4ed6\u63a5\u53d7\u9999\u6e2f\u57ce\u5e02\u5927\u5b66\u8bb2\u5ea7\u6559\u6388\u804c\u4f4d\u5de5\u4f5c\u81f3\u4eca\uff0c\u5728\u8be5\u6821\u6210\u7acb\u4e86\u201c\u590d\u6742\u6027\u4e0e\u590d\u6742\u7f51\u7edc\u201d\u5b66\u672f\u7814\u7a76\u4e2d\u5fc3\u5e76\u4efb\u4e3b\u4efb\u3002\u9648\u5173\u8363\u6559\u6388\u957f\u671f\u4ece\u4e8b\u975e\u7ebf\u6027\u79d1\u5b66\u7814\u7a76\uff0c\u591a\u5e74\u6765\u88ab\u8bc4\u5b9a\u4e3a\u5de5\u7a0b\u5b66\u9ad8\u88ab\u5f15\u7814\u7a76\u4eba\u5458\uff0c\u73b0\u4efb\u201c\u5206\u53c9\u4e0e\u6df7\u6c8c\u201d\u56fd\u9645\u5b66\u672f\u6742\u5fd7\u4e3b\u7f16\u3002\u4ed6\u4e8e1997\u5e74\u88ab\u9009\u4e3aIEEE Fellow\uff0c\u4e8e2008\u30012012\u30012016\u5e74\u83b7\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u4e8c\u7b49\u5956\uff0c2011\u5e74\u83b7\u4fc4\u7f57\u65af\u5723\u5f7c\u5f97\u5821\u56fd\u7acb\u5927\u5b66\u6388\u4e88\u8363\u8a89\u535a\u58eb\u5b66\u4f4d\u548c\u4fc4\u7f57\u65af\u6b27\u62c9\u57fa\u91d1\u4f1a\u9881\u53d1\u6b27\u62c9\u91d1\u8d28\u5956\u7ae0\uff0c2014\u5e74\u83b7\u6cd5\u56fd\u8bfa\u66fc\u5e95\u5927\u5b66\u6388\u4e88\u8363\u8a89\u535a\u58eb\u5b66\u4f4d\uff0c\u5e76\u4e8e2014\u5e74\u5f53\u9009\u4e3a\u6b27\u6d32\u79d1\u5b66\u9662\u9662\u58eb\u30012015\u5e74\u5f53\u9009\u4e3a\u53d1\u5c55\u4e2d\u56fd\u5bb6\u79d1\u5b66\u9662\u9662\u58eb\u3002<\/span><\/section>\n
      \u4e2a\u4eba\u4e3b\u9875\uff1a<\/span><\/section>\n
      http:\/\/www.ee.cityu.edu.hk\/~gchen\/brief.html<\/span><\/section>\n

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      \u4e2a\u4eba\u7b80\u4ecb\uff1a\u738b\u96c4<\/strong>\uff0c\u535a\u58eb\uff0c\u6df1\u5733\u5e02\u6d77\u5916\u9ad8\u5c42\u6b21\u4eba\u624d\uff0c\u5357\u5c71\u9886\u822a\u4eba\u624d\uff0c2004\u5e74\u6bd5\u4e1a\u4e8e\u6e56\u5317\u9ec4\u5188\u4e2d\u5b66\uff0c2009\u5e74\u6bd5\u4e1a\u4e8e\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u6570\u5b66\u7cfb\uff0c\u968f\u540e\u8d74\u9999\u6e2f\u57ce\u5e02\u5927\u5b66\u6df7\u6c8c\u4e0e\u590d\u6742\u7f51\u7edc\u4e2d\u5fc3\u653b\u8bfb\u535a\u58eb\uff0c\u5e08\u4ece\u9648\u5173\u8363\u9662\u58eb\uff1b2014\u5e74\u535a\u58eb\u6bd5\u4e1a\u540e\u83b7\u6df1\u5733\u6d77\u5916\u9ad8\u5c42\u6b21\u4eba\u624d\u5b54\u96c0\u8ba1\u5212\u5f15\u8fdb\uff0c\u52a0\u5165\u6df1\u5733\u5927\u5b66\u9ad8\u7b49\u7814\u7a76\u9662\uff0c\u521b\u7acb\u6df7\u6c8c\u91cf\u5316\u6295\u8d44\u5b9e\u9a8c\u5ba4\uff0c\u7814\u7a76\u57fa\u4e8e\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u3001\u4eba\u5de5\u667a\u80fd\u3001\u5927\u6570\u636e\u5206\u6790\u7b49\u5de5\u5177\u7406\u89e3\u91d1\u878d\u5e02\u573a\u590d\u6742\u6027\u548c\u91cf\u5316\u6295\u8d44\u7b56\u7565\uff0c\u81f4\u529b\u4e8e\u4eba\u5de5\u667a\u80fd\u4e0e\u91d1\u878d\u79d1\u6280\u8de8\u5b66\u79d1\u7814\u7a76\u548c\u590d\u5408\u578b\u4eba\u624d\u7684\u57f9\u517b\u30022020\u5e74\u521b\u7acb\u6df1\u5733\u524d\u6d77\u96c4\u9053\u667a\u80fd\u79d1\u6280\u6709\u9650\u516c\u53f8\u3001\u73e0\u6d77\u6a2a\u7434\u601d\u6e90\u91cf\u5316\u79c1\u52df\u57fa\u91d1\u7ba1\u7406\u5408\u4f19\u4f01\u4e1a(\u6709\u9650\u5408\u4f19)\u62c5\u4efb\u8463\u4e8b\u957f\u3001\u6295\u8d44\u603b\u76d1\u3002<\/span><\/section>\n

      <\/span><\/section>\n
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      \u4e2a\u4eba\u7b80\u4ecb\uff1a\u674e\u6625\u5f6a\uff0c<\/strong><\/span>\u5357\u4eac\u4fe1\u606f\u5de5\u7a0b\u5927\u5b66\u4eba\u5de5\u667a\u80fd\u5b66\u9662\u6559\u6388\u3001\u535a\u58eb\u751f\u5bfc\u5e08\u3002<\/span>\u5357\u4eac\u7406\u5de5\u5927\u5b66\u5de5\u5b66\u535a\u58eb\uff0c\u4e1c\u5357\u5927\u5b66\u535a\u58eb\u540e\uff0c\u7f8e\u56fd\u5a01\u65af\u5eb7\u661f\u5927\u5b66\u8bbf\u95ee\u5b66\u8005\u3002<\/span>\u6c5f\u82cf\u7701\u7b2c\u56db\u671f333\u9ad8\u5c42\u6b21\u4eba\u624d\uff0c\u7269\u7406\u4e0e\u63a7\u5236\u56fd\u9645\u5b66\u4f1a\u4f1a\u5458\uff0c\u201c\u5206\u53c9\u4e0e\u6df7\u6c8c\u201d\u56fd\u9645\u5b66\u672f\u671f\u520a\u7f16\u59d4\uff0c\u4e2d\u56fd\u5bc6\u7801\u5b66\u4f1a\u6df7\u6c8c\u4fdd\u5bc6\u901a\u4fe1\u4e13\u4e1a\u59d4\u5458\u4f1a\u59d4\u5458\uff0c\u4e2d\u56fd\u7535\u5b50\u5b66\u4f1a\u7535\u8def\u4e0e\u7cfb\u7edf\u5206\u4f1a\u6df7\u6c8c\u4e0e\u975e\u7ebf\u6027\u7535\u8def\u4e13\u4e1a\u59d4\u5458\u4f1a\u59d4\u5458\u3002<\/span>\u4e3b\u8981\u4ece\u4e8b\u5fc6\u963b\u7535\u8def\u4e0e\u6df7\u6c8c\u52a8\u529b\u5b66\u53ca\u5176\u5e94\u7528\u7814\u7a76\uff0c\u4e3b\u6301\u4e86\u56fd\u5bb6\u81ea\u7136\u57fa\u91d1\u3001\u7701\u81ea\u7136\u57fa\u91d1\u3001\u7701\u201c333\u4eba\u624d\u201d\u3001\u535a\u58eb\u540e\u7279\u522b\u8d44\u52a9\u7b49\u9879\u76ee\uff0c\u53d1\u8868\u5b66\u672f\u8bba\u6587\u767e\u4f59\u7bc7\uff0c2021\u548c2020\u5e74\u5165\u9009\u7231\u601d\u552f\u5c14\u201c\u4e2d\u56fd\u9ad8\u88ab\u5f15\u5b66\u8005\u699c\u5355\u201d\u3002<\/span>\u4ed6\u662f\u5357\u4fe1\u5927\u6559\u5b66\u540d\u5e08\u548c\u4f18\u79c0\u7814\u7a76\u751f\u5bfc\u5e08\uff0c\u66fe\u83b7\u5f97\u6c5f\u82cf\u7701\u6559\u80b2\u6559\u5b66\u4e0e\u7814\u7a76\u6210\u679c\u4e09\u7b49\u5956\u3001\u56fd\u5bb6\u6559\u5b66\u6210\u679c\u4e8c\u7b49\u5956\u3001\u6c5f\u82cf\u7701\u6559\u5b66\u6210\u679c\u4e00\u7b49\u5956\u548c\u5168\u56fd\u9ad8\u6821\u7535\u5b50\u4fe1\u606f\u6559\u5b66\u6848\u4f8b\u7ade\u8d5b\u4e8c\u7b49\u5956\u7b49\u3002<\/span><\/section>\n

      \u4e2a\u4eba\u4e3b\u9875\uff1a<\/span><\/p>\n

      https:\/\/faculty.nuist.edu.cn\/lichunbiao\/zh_CN\/index.htm<\/span><\/p>\n

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

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      \u5f20\u65ed<\/strong><\/span><\/section>\n
      <\/section>\n
      \u4e2a\u4eba\u7b80\u4ecb\uff1a\u5f20\u65ed<\/strong>\uff0c\u5c71\u4e1c\u5927\u5b66\uff08\u5a01\u6d77\uff09\uff0c\u6570\u5b66\u4e0e\u7edf\u8ba1\u5b66\u9662\uff0c\u7f8e\u56fd\u300a\u6570\u5b66\u8bc4\u8bba\u300b\u4e0e\u5fb7\u56fd\u300a\u6570\u5b66\u6587\u6458\u300b\u8bc4\u8bba\u5458\u3002\u5728 Chaos, Chaos Solitons and Fractals, Discrete and Continuous Dynamical Systems, Ergodic Theory and Dynamical Systems, Fuzzy Sets and Systems,IEEE Transactions on Fuzzy Systems,International Journal of Bifurcation and Chaos, Proceedings of the American Mathematical Society \u7b49\u6742\u5fd7\u53d1\u8868 SCI \u8bba\u6587\u591a\u7bc7\u3002<\/span><\/section>\n

      <\/span><\/section>\n
      \u9a6c\u519b<\/strong><\/span><\/section>\n
      <\/section>\n
      \u4e2a\u4eba\u7b80\u4ecb\uff1a\u9a6c\u519b<\/strong>\uff0c\u5170\u5dde\u7406\u5de5\u5927\u5b66\u6559\u6388\uff0c\u7269\u7406\u5b66\u535a\u58eb(2010.06)\uff0c\u535a\u58eb\u751f\u5bfc\u5e08\uff0c\u5df4\u6e1d\u5b66\u8005\u8bb2\u5ea7\u6559\u6388(2021-2023)\uff0c\u81ea2015\u5e741\u6708\u8d77\u81f3\u4eca\u62c5\u4efbJCR\u4e00\u533a\u671f\u520aNonlinear Dynamics\u526f\u7f16\u8f91(associate editor)\u3002\u4e3b\u8981\u4ece\u4e8b\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u548c\u751f\u7269\u7535\u78c1\u5b66\u65b9\u9762\u7684\u7814\u7a76\uff0c\u6784\u5efa\u4e86\u611f\u77e5\u5149\u3001\u70ed\u3001\u58f0\u97f3\u548c\u7535\u78c1\u573a\u6548\u5e94\u7684\u529f\u80fd\u795e\u7ecf\u5143\u6a21\u578b\uff0c\u89e3\u91ca\u4e86\u7535\u78c1\u8f90\u5c04\u4e0b\u5fc3\u810f\u4f11\u514b\u548c\u6b7b\u4ea1\u7684\u7269\u7406\u5b66\u673a\u5236\uff1b\u4ece\u80fd\u91cf\u89d2\u5ea6\u8bba\u8bc1\u4e86\u795e\u7ecf\u5143\u7a81\u89e6\u53d1\u80b2\u7684\u7269\u7406\u673a\u5236\uff1b\u89e3\u91ca\u4e86\u76f8\u7a7a\u95f4\u538b\u7f29\u6df7\u6c8c\u7cfb\u7edf\u7684\u7269\u7406\u673a\u7406\u53ca\u7535\u8def\u5b9e\u73b0\uff1b\u4ece\u7269\u7406\u89d2\u5ea6\u89e3\u91ca\u529f\u80fd\u795e\u7ecf\u5143\u7535\u8def\u5bf9\u5916\u754c\u5b9e\u9645\u4fe1\u53f7\u9009\u9891\u6ee4\u6ce2\u7684\u673a\u7406\u3002\u4ee5\u7b2c\u4e00\u4f5c\u8005\u548c\u901a\u8baf\u4f5c\u8005\u5728SCI\u6536\u5f55\u671f\u520a\u53d1\u8868\u8bba\u6587180\u4f59\u7bc7\uff0c\u7814\u7a76\u6210\u679c\u5148\u540e\u83b7\u5f97\u7518\u8083\u7701\u81ea\u7136\u79d1\u5b66\u5956\u4e09\u7b49\u5956\u3001\u8d30\u7b49\u5956\u548c\u6d59\u6c5f\u7701\u81ea\u7136\u79d1\u5b66\u5956\u4e09\u7b49\u5956\u5404\u4e00\u9879\uff0cWeb of science\u4e2d\u8bba\u6587H\u6307\u657052\uff0c\u8c37\u6b4c\u5b66\u672f\u8bba\u6587H\u6307\u657055\u3002\u4e3b\u6301\u548c\u5b8c\u6210\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u9879\u76ee4\u9879\uff0c\u53c2\u4e0e\u5b8c\u6210\u56fd\u5bb6\u81ea\u7136\u79d1\u5b66\u57fa\u91d1\u9879\u76ee2\u9879\uff0c\u6388\u6743\u53d1\u660e\u4e13\u52292\u9879\uff0c\u51fa\u7248\u4e13\u84571\u90e8\u3002<\/span><\/section>\n
      \u4e2a\u4eba\u4e3b\u9875\uff1a<\/span><\/section>\n
      https:\/\/www.webofscience.com\/wos\/author\/record\/1609312<\/span> <\/section>\n

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