{"id":60167,"date":"2022-03-09T19:48:05","date_gmt":"2022-03-09T11:48:05","guid":{"rendered":"https:\/\/www.growthhk.cn\/?p=60167"},"modified":"2022-03-09T19:48:08","modified_gmt":"2022-03-09T11:48:08","slug":"%e6%b7%b7%e6%b2%8c%e7%90%86%e8%ae%ba%ef%bc%88chaos-theory%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.growthhk.cn\/quan\/60167.html","title":{"rendered":"\u6df7\u6c8c\u7406\u8bba\uff08Chaos Theory\uff09"},"content":{"rendered":"\n

\u4ec0\u4e48\u662f\u6df7\u6c8c\u7406\u8bba\uff08Chaos Theory\uff09\uff1f \u91ca\u4e49<\/p>\n\n\n\n

Lorenz\u548cPoincar\u00e9\u7684\u6df7\u6c8c\u7406\u8bba\uff0c\u662f\u4e00\u9879\u901a\u8fc7\u7814\u7a76\u590d\u6742\u7684\u52a8\u529b\u7cfb\u7edf\uff0c\u63ed\u793a\u8868\u9762\u65e0\u5e8f\u884c\u4e3a\u6240\u8574\u85cf\u7684\u6709\u5e8f\u6027\uff08\u975e\u6df7\u6c8c\u72b6\u6001\uff09\u7684\u6280\u672f\u3002<\/p>\n\n\n\n

\u201c\u6df7\u6c8c\u7406\u8bba\u662f\u5bf9\u786e\u5b9a\u6027\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u4e2d\u7684\u4e0d\u7a33\u5b9a\u975e\u5468\u671f\u6027\u884c\u4e3a\u7684\u5b9a\u6027\u7814\u7a76\u201d\uff08Kellert\uff0c1993\uff09\u3002\u5728\u6ca1\u6709\u53d8\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u8fd0\u52a8\u662f\u4e00\u9879\u6709\u89c4\u5f8b\u7684\u91cd\u590d\u884c\u4e3a\uff0c\u901a\u8fc7\u7814\u7a76\u8ba4\u8bc6\u8fd9\u4e00\u7cfb\u7edf\u72b6\u6001\uff0c\u975e\u5468\u671f\u6027\u884c\u4e3a\u5c31\u53d8\u6210\u4e86\u53ef\u4ee5\u89c2\u5bdf\u7684\u5bf9\u8c61\u3002\u4e0d\u7a33\u5b9a\u975e\u5468\u671f\u884c\u4e3a\u5219\u590d\u6742\u5f97\u591a\uff1a\u5b83\u4e0d\u505a\u91cd\u590d\u8fd0\u52a8\uff0c\u4e0d\u65ad\u5c55\u73b0\u51fa\u4efb\u4f55\u7ec6\u5fae\u53d8\u5316\u52a8\u4e71\u5bf9\u7cfb\u7edf\u9020\u6210\u7684\u5f71\u54cd\u3002<\/p>\n\n\n\n

\u6839\u636e\u5f53\u4ee3\u6570\u5b66\u7406\u8bba\u7684\u5b9a\u4e49\uff0c\u6df7\u6c8c\u7cfb\u7edf\u5c31\u662f\u5bf9\u201c\u5bf9\u521d\u59cb\u6761\u4ef6\u6781\u5ea6\u654f\u611f\u201d\u7684\u7cfb\u7edf\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e3a\u4e86\u7cbe\u786e\u9884\u6d4b\u7cfb\u7edf\u7684\u672a\u6765\u72b6\u6001\uff0c\u9700\u8981\u77e5\u9053\u5b83\u65e0\u9650\u7cbe\u786e\u7684\u521d\u59cb\u72b6\u6001\uff0c\u5373\u4fbf\u5f88\u5c0f\u7684\u8bef\u5dee\uff0c\u90fd\u5c06\u7acb\u523b\u5bfc\u81f4\u9884\u6d4b\u9519\u8bef\u3002<\/p>\n\n\n\n

\u8fd9\u4e5f\u6b63\u662f\u65e0\u6cd5\u51c6\u786e\u9884\u62a5\u5929\u6c14\u7684\u539f\u56e0\u3002\u6df7\u6c8c\u7406\u8bba\u5df2\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5404\u4e2a\u9886\u57df\uff0c\u5982\u5546\u4e1a\u5468\u671f\u7814\u7a76\u3001\u52a8\u7269\u79cd\u7fa4\u52a8\u529b\u5b66\u3001\u6d41\u4f53\u8fd0\u52a8\u3001\u884c\u661f\u8fd0\u8f6c\u8f68\u9053\u3001\u534a\u5bfc\u4f53\u7535\u6d41\u3001\u533b\u5b66\u9884\u6d4b\uff08\u5982\u766b\u75eb\u53d1\u4f5c\uff09\u4ee5\u53ca\u519b\u5907\u7ade\u8d5b\u5efa\u6a21\u7b49\u7b49\u3002<\/p>\n\n\n\n

20\u4e16\u7eaa60\u5e74\u4ee3\uff0c\u7f8e\u56fd\u9ebb\u7701\u7406\u5de5\u5b66\u9662\u7684\u6c14\u8c61\u5b66\u5bb6Edward Lorenz\u5728\u8ba1\u7b97\u673a\u4e0a\u6a21\u62df\u6c14\u5019\u7c7b\u578b\uff0c \u5f53\u4ed6\u628a\u4e00\u4e2a\u4e2d\u95f4\u503c\u63d0\u9ad8\u7cbe\u5ea6\u518d\u9001\u56de\u6a21\u578b\u4e2d\u53bb\uff0c\u60ca\u5947\u5730\u53d1\u73b0\u672c\u6765\u5f88\u5c0f\u7684\u5dee\u5f02\uff0c\u7adf\u7136\u5b8c\u5168\u6539\u53d8\u4e86\u6a21\u578b\u7ed3\u679c\u3002Lorenz\u8fd9\u4e00\u5076\u7136\u53d1\u73b0\uff0c\u5c31\u662f\u8457\u540d\u7684\u201c\u8774\u8776\u6548\u5e94\u201d \u2014\u2014\u5373\u4fbf\u5f88\u5c0f\u7684\u53d8\u5316\uff0c\u90fd\u80fd\u9020\u6210\u7ed3\u679c\u7684\u5de8\u5927\u4e0d\u540c\uff0c \u5b83\u662f\u6df7\u6c8c\u7406\u8bba\u7684\u7ecf\u5178\u4f8b\u5b50\u2014\u2014 \u9999\u6e2f\u7684\u4e00\u53ea\u8774\u8776\u8f7b\u8f7b\u632f\u52a8\u4e00\u4e0b\u7fc5\u8180\uff0c\u5c31\u6709\u53ef\u80fd\u5728\u7f8e\u56fd\u7684\u5fb7\u514b\u8428\u65af\u5dde\u5f15\u53d1\u4e00\u573a\u9f99\u5377\u98ce\u3002<\/p>\n\n\n\n

\u6839\u636e\u6df7\u6c8c\u7406\u8bba\uff0c\u4f01\u4e1a\u3001\u7ec4\u7ec7\u90fd\u662f\u590d\u6742\u7684\u3001\u52a8\u6001\u7684\u3001\u975e\u7ebf\u6027\u7684\u3001\u5171\u540c\u4f5c\u7528\u7684\u3001\u6781\u4e0d\u5e73\u8861\u7684\u7cfb\u7edf\uff0c \u5b83\u4eec\u7684\u672a\u6765\u8868\u73b0\u4e0d\u53ef\u80fd\u901a\u8fc7\u8fc7\u53bb\u7684\u6216\u73b0\u5728\u7684\u4e8b\u4ef6\u3001\u884c\u4e3a\u6765\u9884\u6d4b\u3002\u5728\u6df7\u6c8c\u72b6\u6001\u4e2d\uff0c\u7ec4\u7ec7\u884c\u4e3a\u65e2\u4e0d\u53ef\u9884\u6d4b\uff08\u6df7\u6c8c\uff09\uff0c\u53c8\u6709\u4e00\u5b9a\u89c4\u5f8b\uff08\u6709\u5e8f\uff09\u3002
\u6df7\u6c8c\u7406\u8bba\u7684\u8d77\u6e90\u3001\u5386\u53f2<\/p>\n\n\n\n

\u6bd4\u5229\u65f6\u7269\u7406\u5316\u5b66\u5bb6\u3001\u8bfa\u8d1d\u5c14\u5956\u5f97\u4e3bIlya Prigogine\u66fe\u6307\u51fa\uff0c\u590d\u6742\u7684\u7ed3\u6784\u5f80\u5f80\u8d77\u6e90\u4e8e\u4e00\u4e9b\u8f83\u4e3a\u7b80\u5355\u7684\u7ed3\u6784\uff0c \u6bd4\u5982\u79e9\u5e8f\u6765\u81ea\u4e8e\u6df7\u4e71\u3002Henry Adams\u4e5f\u66fe\u7528\u8fd9\u6837\u4e00\u53e5\u8bdd\u6765\u63cf\u8ff0\u6df7\u6c8c\u7406\u8bba\uff0c\u201c\u6df7\u6c8c\u54fa\u80b2\u751f\u6d3b\uff0c\u79e9\u5e8f\u57f9\u517b\u4e60\u60ef\u201d\u3002\u4f46\u662f\uff0c\u771f\u6b63\u7684\u6df7\u6c8c\u7406\u8bba\u4e4b\u7236\u5374\u5e94\u8be5\u662fHenri Poincar\u00e9\u3002\u6d77\u738b\u661f\u4e8e1846\u5e74\u88ab\u53d1\u73b0\uff0c\u5728\u8fd9\u4e4b\u524d\u5b83\u7684\u5b58\u5728\u5df2\u7ecf\u901a\u8fc7\u5929\u738b\u661f\u8fd0\u884c\u8f68\u9053\u7684\u504f\u79bb\u88ab\u9884\u6d4b\u51fa\u6765\u3002<\/p>\n\n\n\n

\u632a\u5a01\u56fd\u738b\u5965\u65af\u5361\u4e8c\u4e16\u5c31\u6b64\u60ac\u8d4f\u8bba\u8bc1\u201c\u592a\u9633\u7cfb\u5230\u5e95\u662f\u4e0d\u662f\u9759\u6b62\u7684\u201d\u3002Poincar\u00e9\u63d0\u4f9b\u4e86\u4ed6\u7684\u65b9\u6cd5\uff0c\u8d62\u5f97\u4e86\u8be5\u5956\u91d1\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u4ed6\u7684\u597d\u53cb\u5728\u4ed6\u7684\u8ba1\u7b97\u91cc\u53d1\u73b0\u4e86\u4e00\u4e2a\u9519\u8bef\uff0c\u5956\u91d1\u53c8\u4e00\u5ea6\u88ab\u53d6\u56de\uff0c\u76f4\u5230\u4ed6\u53c8\u62ff\u51fa\u4e86\u65b0\u7ed3\u8bba\u3002\u4ed6\u7684\u65b0\u7ed3\u8bba\u5c31\u662f\uff0c\u5728\u8fd9\u4e00\u95ee\u9898\u4e0a\u6839\u672c\u6ca1\u6709\u7ed3\u8bba\uff0c \u751a\u81f3\u8fde\u725b\u987f\u5b9a\u5f8b\u4e5f\u4e0d\u80fd\u89e3\u51b3\u8fd9\u4e00\u96be\u9898\u3002Poincar\u00e9\u6253\u7b97\u4ece\u8fd9\u4e2a\u7cfb\u7edf\u4e2d\u627e\u51fa\u4e00\u5b9a\u7684\u79e9\u5e8f\u6765\uff0c\u4f46\u662f\u65e0\u529f\u800c\u8fd4\u3002\u5230\u4e8620\u4e16\u7eaa60\u5e74\u4ee3\uff0c\u6df7\u6c8c\u7406\u8bba\u57fa\u672c\u6210\u5f62\u3002\u5728\u8fd9\u4e00\u65f6\u671f\uff0cEdward Lorenz\u5b8c\u6210\u4e86\u5927\u91cf\u7684\u5b9e\u8bc1\u5de5\u4f5c\uff0c \u7f8e\u56fd\u9a6c\u91cc\u5170\u5927\u5b66\u7684\u5e94\u7528\u6570\u5b66\u5bb6Jim Yorke\u6700\u7ec8\u5c06\u8fd9\u4e00\u7406\u8bba\u5b9a\u540d\u4e3a\u6df7\u6c8c\u7406\u8bba\uff08Ruelle, 1991\uff09\u3002<\/p>\n\n\n\n

\u6df7\u6c8c\u7406\u8bba\u7684\u8ba1\u7b97\u3002 \u516c\u5f0f<\/p>\n\n\n\n

\u4e3a\u4e86\u80fd\u591f\u628a\u6df7\u6c8c\u7406\u8bba\u7528\u4e8e\u5b9e\u8df5\uff0c\u9700\u8981\u6709\u4e00\u4e2a\u5355\u72ec\u7684\u6d4b\u5b9a\u53d8\u91cfx(n) = x(t0 + nt)\u63d0\u4f9b\u4e00\u4e2an\u7ef4\u7a7a\u95f4\uff08\u6216\u79f0\u62d3\u6251\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662f\u7cfb\u7edf\u7684\u591a\u5143\u72b6\u6001\u77e2\u91cf\u7a7a\u95f4\uff09\u3002\u8fd9\u91cc\uff0ct0\u4ee3\u8868\u8d77\u59cb\u65f6\u95f4\uff0ct\u4ee3\u8868\u5176\u524d\u7f6e\u65f6\u95f4\u3002\u6df7\u6c8c\u7cfb\u7edf\u7684\u62d3\u6251\u7a7a\u95f4\u9700\u89814\u4e2a\u7ef4\u5ea6\u3002\u7136\u540e\uff0c\u5f53\u4f60\u89c2\u5bdf\u4e00\u4e2a\u7cfb\u7edf\u7684\u957f\u671f\u8fd0\u4f5c\u60c5\u51b5\u65f6\uff0c\u4f60\u5c31\u4f1a\u53d1\u73b0\u5b83\u6240\u5f62\u6210\u7684\u975e\u7ebf\u6027\u65f6\u95f4\u5e8f\u5217\uff0c\u6700\u7ec8\u5728\u56f4\u7ed5\u62d3\u6251\u7a7a\u95f4\u7684\u67d0\u4e2a\u660e\u786e\u5f62\u72b6\u6e38\u8361\uff0c\u901a\u8fc7\u5b83\u5373\u53ef\u9884\u6d4b\u7cfb\u7edf\u7684\u672a\u6765\u72b6\u6001\uff08Solomatine,et al, 2001\uff09\u3002<\/p>\n\n\n\n

\u6df7\u6c8c\u7406\u8bba\u7684\u8fd0\u7528\u3002 \u5e94\u7528<\/p>\n\n\n\n

\u6df7\u6c8c\u7406\u8bba\u5df2\u7ecf\u6210\u529f\u89e3\u91ca\u4e86\u5404\u79cd\u5404\u6837\u7684\u81ea\u7136\u73b0\u8c61\u548c\u4eba\u7c7b\u884c\u4e3a\u3002\u4f8b\u5982\uff1a<\/p>\n\n\n\n