{"id":15681,"date":"2013-12-17T22:08:12","date_gmt":"2013-12-17T14:08:12","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=15681"},"modified":"2017-07-27T10:45:55","modified_gmt":"2017-07-27T02:45:55","slug":"%e3%80%90%e7%89%b9%e7%a8%bf%e3%80%91%e7%8f%be%e5%af%a6%e7%94%9f%e6%b4%bb%e7%9a%84%e6%a8%a1%e6%93%ac%e8%be%b2%e5%a0%b4%e2%94%80%e2%94%80%e6%bc%ab%e8%ab%87%e7%94%9f%e6%85%8b%e7%b3%bb%e4%b8%ad%e7%9a%84","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=15681","title":{"rendered":"\u3010\u63a2\u7d22\u5341\u3011\u73fe\u5be6\u751f\u6d3b\u7684\u6a21\u64ec\u8fb2\u5834\u2500\u2500\u6f2b\u8ac7\u751f\u614b\u7cfb\u4e2d\u7684\u65cf\u7fa4\u6578\u91cf\u8b8a\u5316"},"content":{"rendered":"<h3 style=\"text-align: center;\"><strong><span style=\"color: #800000;\">\u7b2c\u4e03\u8b1b\u2027\u7279\u7a3f<\/span><\/strong><\/h3>\n<p><span style=\"color: #008080;\"><strong>\u25a0 \u300c\u7576\u7cfb\u7d71\u8907\u96dc\u6642\uff0c\u601d\u8003\u65b9\u5411\u5c31\u8981\u6539\u8b8a\u3002\u5f9e\u53e6\u4e00\u500b\u89d2\u5ea6\u53bb\u601d\u8003\u554f\u984c\u3002\u300d\u2500\u2500\u5289\u7dad\u4e2d\u8001\u5e2b\u6b63\u662f\u5229\u7528\u300c\u6a21\u578b\u300d\u4f86\u62bd\u8c61\u63cf\u8ff0\u6211\u5011\u7684\u73fe\u5be6\u4e16\u754c\uff0c\u63e3\u6469\u98df\u7269\u7db2\u5f62\u6210\u7684\u53ef\u80fd\u6a5f\u5236\u3002<\/strong><\/span><\/p>\n<figure id=\"attachment_15752\" aria-describedby=\"caption-attachment-15752\" style=\"width: 549px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058.jpg\"><img fetchpriority=\"high\" decoding=\"async\" class=\" wp-image-15752 \" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058.jpg\" alt=\"ctr058\" width=\"549\" height=\"382\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058.jpg 858w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058-300x208.jpg 300w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058-800x557.jpg 800w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/ctr058-600x417.jpg 600w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/a><figcaption id=\"caption-attachment-15752\" class=\"wp-caption-text\">\u5716\u7247\u4f86\u6e90|Getty Image<\/figcaption><\/figure>\n<p style=\"text-align: left;\"><strong>\u64b0\u6587\u2502<\/strong>\u90ed\u51a0\u5ef7<\/p>\n<p><strong>\u5c0d\u73fe\u5be6\u4e16\u754c\u7684\u62bd\u8c61\u63cf\u8ff0\u2014\u5982\u4f55\u5efa\u7acb\u300c\u7406\u8ad6\u300d\uff1f<\/strong><br \/>\n\u751f\u614b\u6a21\u578b\u7684\u5efa\u7acb\uff0c\u53ef\u4ee5\u5f9e\u6700\u7c21\u55ae\u7684\u56db\u5247\u904b\u7b97\u958b\u59cb\u3002<i>N<sub>t<\/sub><\/i>\u4ee3\u8868 t \u6642\u9593\u9ede\u7684\u65cf\u7fa4\u6578\u91cf\uff0c<i>IN<\/i><sub><sub>\u0394<i>t \u00a0<\/i><\/sub><\/sub> \u4ee3\u8868\u65cf\u7fa4\u5728 \u0394t \u671f\u9593\u6240\u589e\u52a0\u7684\u91cf\uff0c<em>OUT<\/em><i><\/i><sub><sub>\u0394<i>t \u00a0<\/i><\/sub><\/sub> \u4ee3\u8868\u65cf\u7fa4\u5728\u0394<i>t\u00a0<\/i> \u671f\u9593\u6240\u6e1b\u5c11\u7684\u91cf\u3002\u5c31\u662f\u6642\u9593\u9ede\u7684\u65cf\u7fa4\u6578\u91cf\u3002<i>N\u00a0<sub>t+\u0394<i>t\u00a0<\/i><\/sub><\/i>\u5c31\u662f\u00a0<i>t+\u0394<i>t \u00a0<\/i><\/i>\u6642\u9593\u9ede\u7684\u65cf\u7fa4\u6578\u91cf\u3002<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter wp-image-15678\" style=\"border: 0px;\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72471.png\" alt=\"\u5716\u72471\" width=\"288.6\" height=\"36.6\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72471.png 481w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72471-300x38.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u800c\u7406\u8ad6\u7684\u91cd\u9ede\u5c31\u5728\u65bc\uff0c\u5982\u4f55\u53bb\u63cf\u8ff0\u00a0<i>IN<\/i><sub><sub>\u0394<i>t \u00a0<\/i><\/sub><\/sub>\u548c\u00a0<em>OUT<\/em><i><\/i><sub><sub>\u0394<i>t \u00a0<\/i><\/sub><\/sub>\uff1f\u6211\u5011\u5047\u8a2d\u6bcf\u500b\u500b\u9ad4\u5728\u55ae\u4f4d\u6642\u9593\u53ef\u4ee5\u7522\u751fb\u500b\u5f8c\u4ee3<em> b<\/em>\u00b7<i>N<sub>t<\/sub><\/i>\u00a0\u00b7\u0394<i>t<\/i>\uff0c\u800c\u5728\u55ae\u4f4d\u6642\u9593\u6709d \u6bd4\u4f8b\u7684\u500b\u9ad4\u6703\u6b7b\u4ea1 d\u00b7<i>N<sub>t<\/sub><\/i>\u00a0\u00b7\u0394<i>t<\/i>\u3002\u5982\u6b64\uff0c\u6211\u5011\u5c31\u5f97\u5230\u65cf\u7fa4\u7684\u300c\u51fa\u751f\u8207\u6b7b\u4ea1\u6a21\u578b\u300d\uff1a<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-15683\" style=\"border: 0px;\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72472.png\" alt=\"\u5716\u72472\" width=\"365.4\" height=\"36.6\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72472.png 609w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72472-300x30.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><!--more--><\/p>\n<p>&nbsp;<\/p>\n<p>\u800c\u6211\u5011\u6839\u64da\u00a0\u0394<i>t\u00a0<\/i>\u7684\u9577\u77ed\uff0c\u53c8\u53ef\u4ee5\u5206\u70ba\u0394<i>t <\/i>=1\u7684\u96e2\u6563\u578b\u6a21\u578b\uff08Discrete time\uff09\u548c\u00a0\u0394<i>t\u00a0<\/i>\u975e\u5e38\u5c0f\uff08\u00a0\u0394<i>t<\/i> ~0\uff09\u7684\u9023\u7e8c\u578b\u6a21\u578b\uff08Continuous time\uff09\u5169\u985e\u3002\u6211\u5011\u53ea\u8981\u7d66\u5b9a\u521d\u59cb\u503c<i>N<span style=\"font-size: 12px;\">0\u00a0<\/span><\/i>\u548c\u53c3\u6578b\u3001d\uff0c\u5c31\u53ef\u4ee5\u7e6a\u88fd\u51fa\u591a\u7d44\u6a21\u578b\u7684\u7d50\u679c\u3002\u6211\u5011\u4ee5<i>N<sub>t<\/sub><\/i>\u00a0\u5c0d\u6642\u9593 t\u4f5c\u5716\uff0c\u5229\u7528\u66f2\u7dda\u5716\u4f86\u8868\u793a\u65cf\u7fa4\u6578\u91cf\u7684\u8b8a\u5316\u3002<b>\u5145\u6eff\u8b8a\u7570\u6027\u548c\u4e0d\u78ba\u5b9a\u6027\u7684\u73fe\u5be6\u4e16\u754c<\/b>\u70ba\u89e3\u91cb\u771f\u5be6\u4e16\u754c\u7684\u6578\u64da\uff0c\u6211\u5011\u5efa\u7acb\u300c\u96a8\u6a5f\u6a21\u578b\uff08Stochastic\uff09\u300d\uff0c\u7528\u4f86\u63cf\u8ff0\u8b8a\u7570\u6027\u548c\u4e0d\u78ba\u5b9a\u6027\uff1a\u4e00\u3001\u5230\u4e0b\u6b21\u767c\u751f\u4e8b\u60c5\u7684\u6642\u9593\u8981\u7b49\u591a\u4e45\uff1f\u4e5f\u5c31\u662f\u4e0a\u8ff0\u7684\u0394<i>t\u00a0<\/i>\u3002\u4e8c\u3001\u5230\u4e0b\u6b21\u767c\u751f\u4e8b\u60c5\u7684\u6642\u5019\u4ec0\u9ebc\u6709\u53ef\u80fd\u6703\u767c\u751f\uff1f\u5c31\u4e0a\u8ff0\u7684\u51fa\u751f\u6b7b\u4ea1\u6a21\u578b\u800c\u8a00\uff0c\u6b64\u6a21\u578b\u4e2d\u6240\u767c\u751f\u7684\u300c\u4e8b\u60c5\u300d\u53ea\u6709\u5169\u7a2e\u53ef\u80fd\uff1a\u51fa\u751f\u3001\u6b7b\u4ea1\u3002\u52a0\u5165\u53c3\u6578\u5f8c\u7684\u7d50\u679c\uff0c\u51fa\u4e4e\u6211\u5011\u7684\u9810\u671f\uff0c\u6578\u91cf\u5c0d\u6642\u9593\u4f5c\u5716\u672c\u662f\u4e00\u689d\u6c34\u5e73\u7dda\uff08\u65cf\u7fa4\u6578\u91cf\u6301\u5e73\uff09\u7684\u5716\u8868\uff0c\u96fb\u8166\u537b\u6a21\u64ec\u51fa\u300c\u5728\u51fa\u751f\u7387\u7b49\u65bc\u6b7b\u4ea1\u7387\u7684\u60c5\u6cc1\u4e0b\uff0c\u65cf\u7fa4\u6709\u53ef\u80fd\u6ec5\u4ea1\u3002\u300d\u70ba\u4ec0\u9ebc\u5462\uff1f\u8001\u5e2b\u89e3\u91cb\uff1a\u300c\u65cf\u7fa4\u6578\u91cf\u5f88\u5c11\u7684\u6642\u5019\uff0c\u65cf\u7fa4\u6703\u5bb9\u6613\u6ec5\u4ea1\u3002\u300d<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u66ff\u7c21\u6613\u6a21\u578b\u589e\u52a0\u8b8a\u6578<\/b><\/p>\n<p>\u7576\u65cf\u7fa4\u6578\u91cf\u589e\u52a0\u6642\uff0c\u500b\u9ad4\u5c31\u6703\u6108\u4f86\u6108\u96e3\u627e\u5230\u98df\u7269\u3002\u6240\u4ee5\u7528\u4f86\u63cf\u8ff0\u65cf\u7fa4\u5728\u55ae\u4f4d\u6642\u9593\u4e2d\u500b\u9ad4\u6b7b\u4ea1\u6bd4\u4f8b\u7684d \u5c31\u6703\u8b8a\u6210\uff1a d=d<sub>0<\/sub>+d<sub>1<\/sub>\u00b7<i>N<sub>t<\/sub><\/i>\u00a0\u3002<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"aligncenter wp-image-15686\" style=\"border: 0px;\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72473.png\" alt=\"\u5716\u72473\" width=\"604.1\" height=\"26.6\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72473.png 863w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72473-300x13.png 300w\" sizes=\"(max-width: 863px) 100vw, 863px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>\u800c\u9019\u7d44\u6a21\u578b\u4e2d\uff0c\u5047\u82e5\u662f\u96e2\u6563\u578b\u7684\u6642\u9593\u9593\u9694\uff08\u0394<i>t<\/i>\u00a0=1\uff09\u3002\u7c21\u55ae\u7684\u55ae\u7269\u7a2e\u6a21\u578b\uff0c\u5c31\u6709\u76f8\u7576\u8c50\u5bcc\u7684\u73fe\u8c61\u3002\u7576b=1\u7684\u6642\u5019\uff0c\u65cf\u7fa4\u6578\u91cf\u6703\u5448\u73fe\u6307\u6578\u589e\u52a0\uff0c\u800c\u5230\u4e00\u5b9a\u7684\u503c\u5f8c\u6703\u7a69\u5b9a\u4e0b\u4f86\u3002\u53ef\u662f\u7576b=2\u7684\u4e4b\u5f8c\uff0c\u6703\u5448\u73fe\u9707\u76ea\u5f8c\u8da8\u65bc\u4e00\u500b\u7a69\u5b9a\u503c\u7684\u904e\u7a0b\u3002b=2.5 \u6642\uff0c\u65cf\u7fa4\u6578\u91cf\u6703\u5728\u4e8c\u500b\u9ede\u4e4b\u9593\u9707\u76ea\u3002b=2.6\u6642\uff0c\u5247\u6703\u5728\u56db\u9ede\u9707\u76ea\uff084-point cycles\uff09\u3002\u800c\u96a8\u8457b\u503c\u589e\u52a0\uff0c\u9707\u76ea\u7684\u9ede\u9010\u6f38\u589e\u52a0\u3002\u96fb\u8166\u6a21\u64ec\u7684\u7d50\u679c\u544a\u8a34\u6211\u5011\uff0cb\u503c\u589e\u52a0\u6700\u7d42\u7684\u7d50\u679c\uff0c\u65cf\u7fa4\u6578\u91cf\u6703\u5b8c\u5168\u5931\u5e8f\uff08chaotic\uff09\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u5728\u9023\u7e8c\u6a21\u578b\uff08\u00a0\u0394<i>t<\/i>\u00a0~0\uff09\u4e2d\uff0cb\u503c\u7684\u589e\u52a0\u5c0d\u55ae\u7269\u7a2e\u6578\u91cf\u7684\u5f71\u97ff\uff0c\u4e0d\u6703\u5448\u73fe\u4efb\u4f55\u9031\u671f\u6027\u8b8a\u5316\uff0c\u96a8\u8457\u6642\u9593\uff0c\u6700\u7d42\u90fd\u6703\u7a69\u5b9a\u5230\u4e00\u500b\u56fa\u5b9a\u7684\u503c\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u5c0b\u627e\u5e73\u8861\u9ede<\/b><\/p>\n<p>\u9019\u7a2e\u8f03\u8907\u96dc\u7684\u51fa\u751f\u3001\u6b7b\u4ea1\u6a21\u578b\uff0c\u662f\u5c6c\u65bc\u4e00\u7a2e\u81ea\u5f8b\uff08\u81ea\u8abf\uff09\u6a21\u578b\u3002\u6a21\u578b\u7684\u7d50\u679c\u662f\u8b93\u65cf\u7fa4\u6578\u91cf\u5f80\u67d0\u7279\u5b9a\u7684\u6578\u503c\u903c\u8fd1\uff0c\u6216\u8005\u662f\u5728\u67d0\u4e9b\u6578\u503c\u4e4b\u9593\u9707\u76ea\u3002\u9019\u4e9b\u503c\u6211\u5011\u7a31\u70ba\u300c\u5e73\u8861\u9ede\uff08equilibrium point\uff09\u300d\u3002<\/p>\n<p>\u7576\u65cf\u7fa4\u6578\u91cf\u7dad\u6301\u5728\u5e73\u8861\u9ede\u00a0<em>N*\u00a0<\/em>\u4e0d\u518d\u8b8a\u5316\u6642[1]\uff0c\u6211\u5011\u4ee5\u96e2\u6563\u6a21\u578b\uff08\u0394<i>t<\/i>\u00a0=1\uff09\u7684\u5e73\u8861\u9ede\u00a0<em>N*\u00a0<\/em>\u70ba\u4f8b\uff0c\u8a66\u8457\u89e3\u51fa\u00a0<em>N*\u00a0<\/em>\u3002<\/p>\n<p style=\"text-align: left;\"><img decoding=\"async\" class=\"aligncenter wp-image-15688\" style=\"border: 0px;\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72474.png\" alt=\"\u5716\u72474\" width=\"570.24\" height=\"124.08\" srcset=\"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72474.png 864w, https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2013\/12\/\u5716\u72474-300x65.png 300w\" sizes=\"(max-width: 864px) 100vw, 864px\" \/><br \/>\n<b>\u96d9\u7269\u7a2e\u5982\u4f55\u80fd\u5920\u5171\u5b58\uff1f<\/b><\/p>\n<p>\u6211\u5011\u5047\u8a2d\u5169\u7a2e\u7269\u7a2eA\u548c\u7269\u7a2eB\u5229\u7528\u76f8\u540c\u7684\u8cc7\u6e90\uff0c\u6211\u5011\u53ef\u4ee5\u5f97\u5230\u7269\u7a2eA\u548c\u7269\u7a2eB\u5404\u81ea\u7684\u51fa\u751f\u6b7b\u4ea1\u6a21\u578b\u3002<\/p>\n<p>\u56e0\u70ba\u7269\u7a2e\u4e4b\u9593\u7684\u7af6\u722d\u529b\u9700\u8981\u52a0\u4ee5\u63cf\u8ff0\uff0c\u6211\u5011\u5f15\u9032\u53c3\u6578 \u03b1\u00a0<em><sub>BA\u00a0<\/sub><\/em>\u548c\u00a0\u03b1\u00a0<em><sub>AB<\/sub><\/em>\u3002\u03b1\u00a0<em><sub>BA\u00a0<\/sub><\/em>\u4ee3\u8868\u6bcf\u7269\u7a2eB\u7684\u500b\u9ad4\u6578\u91cf\u76f8\u7576\u65bc\u7269\u7a2eA\u7684\u500b\u9ad4\u6578\u91cf\u3002\u5047\u82e5\u03b1\u00a0<em><sub>BA\u00a0<\/sub><\/em>=3\uff0c\u5c31\u4ee3\u8868\u4e00\u500b\u7269\u7a2eB\u76f8\u7576\u65bc\u4e09\u500b\u7269\u7a2eA\u7684\u500b\u9ad4\uff0c\u4ee3\u8868\u7269\u7a2eB\u4f54\u6709\u512a\u52e2\u3002<\/p>\n<p>\u7269\u7a2eA\u7684Zero-isocline\u662f\u4e8c\u7dad\u7a7a\u9593\u7576\u4e2d\u7684\u4e00\u689d\u66f2\u7dda\uff0c\u7528\u4f86\u63cf\u8ff0\u7269\u7a2eA\u548c\u7269\u7a2eB\u6578\u91cf\u7684\u8b8a\u5316\u00a0<i>N<sub>A<\/sub>-<i>N<sub>B<\/sub><\/i><\/i>\u3002\u5728\u6b64\u7dda\uff08<i>N<sub>A<\/sub>-<i>N<sub>B\u00a0<\/sub><\/i><\/i>=0\uff09\u4e0a\u7269\u7a2eA\u7684\u65cf\u7fa4\u8b8a\u5316\u91cf\u662f0\uff0c\u800c\u7dda\u7684\u4e00\u65b9\u7684\u7269\u7a2eA\u7684\u65cf\u7fa4\u6578\u91cf\u8b8a\u5316\u662f\u589e\u52a0\uff0c\u53e6\u4e00\u5074\u7269\u7a2eA\u7684\u65cf\u7fa4\u6578\u91cf\u8b8a\u5316\u662f\u6e1b\u5c11\u7684\u3002\u540c\u7406\uff0c\u6211\u5011\u4e5f\u80fd\u7e6a\u88fd\u51fa\u7269\u7a2eB\u7684Zero-isocline\u3002<\/p>\n<p>\u56e0\u8457\u00a0\u03b1\u00a0<em><sub>BA<\/sub><\/em>\u548c\u00a0\u03b1\u00a0<em><sub>AB\u00a0<\/sub><\/em>\u6578\u503c\u7684\u4e0d\u540c\uff0c\u5169\u689d\u7dda\u4e4b\u9593\u7684\u95dc\u4fc2\u6709\u6578\u7a2e\uff1a\u7269\u7a2eA\u548c\u7269\u7a2eB\u5171\u5b58\u3001\u7269\u7a2eB\u7368\u8d0f\uff0c\u4ee5\u53ca\u53ea\u6709\u4e00\u500b\u7269\u7a2e\u8d0f\uff08\u600e\u9ebc\u8d0f\u8981\u770b\u51fa\u767c\u9ede\uff09\u3002<\/p>\n<p>\u96d9\u7269\u7a2e\u5171\u5b58\u7684\u689d\u4ef6\uff0c\u662f\u7269\u7a2e\u81ea\u5df1\u7d66\u81ea\u5df1\u7684\u8ca0\u4f5c\u7528\uff0c\u8981\u5927\u65bc\u7d66\u53e6\u4e00\u500b\u7269\u7a2e\u7684\u526f\u4f5c\u7528\u3002\u300c\u5169\u500b\u5718\u9ad4\u5167\u5982\u679c\u90fd\u6709\u5167\u9b28\uff0c\u5c31\u6c92\u6709\u6642\u9593\u53bb\u653b\u64ca\u53e6\u4e00\u500b\u5718\u9ad4\uff0c\u5982\u6b64\u4e00\u4f86\u96d9\u65b9\u5c31\u80fd\u5920\u5171\u5b58\u3002\u300d<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u7375\u7269\uff08X<\/b><b>\uff09\u548c\u7375\u6bba\u8005\uff08Y<\/b><b>\uff09\u6a21\u578b<\/b><\/p>\n<p>\u6211\u5011\u5f9e\u51fa\u751f\u6b7b\u4ea1\u6a21\u578b\u51fa\u767c\u3002\u7375\u7269X\u7684\u6b7b\u4ea1\u7387\u56e0\u70ba\u906d\u7375\u6bba\u800c\u589e\u52a0\u3002\u7375\u6bba\u8005Y\u7375\u6bba\u7684\u6240\u5f97\u900f\u904e\u53c3\u6578\u8f49\u63db\u6210\u7375\u6bba\u8005Y\u7684\u51fa\u751f\u7387\u3002\u4e26\u627e\u51fa\u7375\u7269\u548c\u7375\u6bba\u8005\u7684Zero-isocline\u3002\u6211\u5011\u53ef\u4ee5\u767c\u73fe\u5f97\u51fa\u4f86\u7684\u5716\u5f62\uff0c\u5e73\u5747\u5411\u91cf\u7684\u8b8a\u5316\uff0c\u4f3c\u4e4e\u5728\u300c\u7e5e\u5708\u5708\u300d\u3002\u65cf\u7fa4\u6578\u91cf\u7684\u8b8a\u5316\u5c0d\u6642\u9593\u4f5c\u5716\uff0c\u6709\u9031\u671f\u6027\u8b8a\u5316\uff08neutral cycles\uff09\uff0c\u9019\u500b\u9031\u671f\u6027\u8b8a\u5316\uff0c\u6703\u53d6\u6c7a\u65bc\u300c\u51fa\u767c\u9ede\u300d\u3002\u4e0d\u540c\u7684\u521d\u59cb\u503c\u6703\u5c0e\u81f4\u4e0d\u540c\u7684\u7d50\u679c\u3002<\/p>\n<p>\u4f46\u662f\uff0c\u5982\u679c\u9019\u500b\u6a21\u578b\u662f\u300c\u96a8\u6a5f\u6a21\u578b\u300d\uff0c\u70ba\u4ec0\u9ebc\u96fb\u8166\u6a21\u64ec\u7684\u7d50\u679c\u537b\u6c92\u6709\u8fa6\u6cd5\u51fa\u73fe\u9031\u671f\u6027\u8b8a\u5316\uff1f\u300c\u56e0\u70ba\u65cf\u7fa4\u6578\u91cf\u5f88\u5c11\u7684\u6642\u5019\uff0c\u65cf\u7fa4\u6703\u5bb9\u6613\u6ec5\u4ea1\u3002\u300d\u56e0\u6b64\uff0c\u7576\u6211\u5011\u52a0\u5165\u4e0d\u78ba\u5b9a\u6027\u548c\u8b8a\u7570\u6027\u5f8c\uff0c\u6a21\u578b\u5f88\u96e3\u5448\u73fe\u6c38\u6046\u7684\u9031\u671f\u6027\u6578\u91cf\u8b8a\u5316\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u5982\u4f55\u8b93\u7269\u7a2e\u80fd\u5920\u5171\u5b58\uff1f<\/b><\/p>\n<p><strong>\u4e00\u3001\u5169\u500b\u7375\u6bba\u8005\u5171\u540c\u7af6\u722d\u76f8\u540c\u7684\u7375\u7269\uff0c\u5169\u4f4d\u7375\u6bba\u8005\u4e4b\u9593\u53ef\u4ee5\u5171\u5b58\u55ce\uff1f<\/strong><\/p>\n<p>\u96fb\u8166\u6a21\u64ec\u7684\u7d50\u679c\uff0c\u5176\u4e2d\u4e00\u500b\u7375\u6bba\u8005\u6703\u56e0\u70ba\u7375\u7269\u7684\u6578\u91cf\u6709\u9650\uff0c\u800c\u906d\u9047\u6ec5\u4ea1\u3002<\/p>\n<p>\u4f46\u662f\u73fe\u5be6\u4e16\u754c\u7576\u4e2d\uff0c\u537b\u6709\u8a31\u591a\u7af6\u722d\u76f8\u540c\u7375\u7269\u7684\u7375\u6bba\u8005\u5f97\u4ee5\u5171\u5b58\u3002\u53ef\u80fd\u7684\u539f\u56e0\u6709\uff1a\u5169\u500b\u7375\u6bba\u8005\u751f\u5b58\u5728\u4e0d\u540c\u7684\u68f2\u606f\u5730\uff0c\u6216\u662f\u98df\u7528\u76f8\u540c\u7375\u7269\u4e0d\u540c\u7684\u6210\u9577\u968e\u6bb5\u3002\u4e5f\u53ef\u80fd\u662f\u7375\u6bba\u8005\u4e4b\u9593\u6709\u8457\u300c\u7fa4\u805a\u6548\u61c9\uff08aggrcgation\uff09\u300d\uff0c\u9020\u6210\u8cc7\u6e90\uff08\u7375\u7269\uff09\u5340\u5206\u3002<\/p>\n<p>\u6240\u4ee5\uff0c\u7af6\u722d\u8005\u7684\u5171\u5b58\u8207\u5426\uff0c\u53d6\u6c7a\u65bc\u4ed6\u5011\u7af6\u722d\u8cc7\u6e90\uff08\u7375\u7269\uff09\u7684\u76f8\u4f3c\u7a0b\u5ea6\u3002<\/p>\n<p><strong>\u4e8c\u3001\u96d9\u7375\u7269\u88ab\u76f8\u540c\u7684\u7375\u6bba\u8005\u6240\u7375\u6bba\uff0c\u8981\u76f8\u4e92\u7af6\u722d\u300c\u6c92\u5929\u6575\u7684\u7a7a\u9593\u300d\uff0c\u5247\u9019\u5169\u88ab\u7375\u6bba\u7684\u7269\u7a2e\uff0c\u53ef\u4ee5\u5171\u5b58\u55ce\uff1f<\/strong><\/p>\n<p>\u96fb\u8166\u6a21\u64ec\u7684\u7d50\u679c\uff0c\u5176\u4e2d\u4e00\u500b\u7375\u7269\u5fc5\u5b9a\u6703\u8d70\u5411\u6ec5\u5b8c\u3002<\/p>\n<p>\u4e0d\u904e\u771f\u5be6\u81ea\u7136\u754c\u4e2d\u6709\u4e0d\u540c\u7684\u7375\u7269\u5171\u5b58\u7684\u4f8b\u5b50\u3002\u9019\u53ef\u80fd\u6b78\u529f\u65bc\u300c\u5e87\u8b77\u6240\uff08refuge\uff09\u300d\u7684\u529f\u52de\uff0c\u8b93\u7375\u7269\u4e0d\u5b8c\u5168\u88ab\u7375\u6bba\u8005\u6240\u7375\u6bba\uff0c\u9020\u6210\u7269\u7a2e\u5171\u5b58\u7684\u6548\u61c9\u3002<\/p>\n<p><strong>\u4e09\u3001\u98df\u7269\u93c8\u6a21\u578b\u3002\u7269\u7a2eA\u88ab\u7269\u7a2eB\u5403\uff0c\u7269\u7a2eB\u53c8\u88ab\u7269\u7a2eC\u5403\u3002\u9019\u7a2e\u60c5\u6cc1\u4e0b\uff0c\u4e09\u7269\u7a2e\u53ef\u4ee5\u5171\u5b58\u55ce\uff1f<\/strong><\/p>\n<p>\u6211\u5011\u5f97\u5230\u7684\u6a21\u64ec\u7d50\u679c\u662f\uff1a\u53ef\u4ee5\u5171\u5b58\u3002\u7269\u7a2eC\u6703\u58d3\u5236\u7269\u7a2eB\uff0c\u9020\u5c31\u7269\u7a2eA\u6703\u7121\u9650\u6210\u9577\u3002\u300c\u4e0a\u7d1a\u7375\u6bba\u8005\u628a\u4e0b\u7d1a\u7375\u7269\u5f9e\u4e2d\u9593\u7375\u6bba\u8005\u91cb\u653e\u51fa\u4f86\u300d\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u591a\u7269\u7a2e\u6a21\u578b<\/b><\/p>\n<p>\u5f9e\u4e0a\u8ff0\u7684\u300c\u4f8b\u5b50\u4e00\u300d[2]\u7576\u4e2d\u6211\u5011\u5f97\u77e5\uff0c\u7576\u7269\u7a2eB\u548c\u7269\u7a2eC\u5171\u540c\u7af6\u722d\u7269\u7a2eA\u6642\uff0c\u7269\u7a2eB\u548c\u7269\u7a2eC\u7121\u6cd5\u5171\u5b58\u3002\u56e0\u6b64\uff0c\u6211\u5011\u5617\u8a66\u52a0\u5165\u7269\u7a2eD\u4f86\u6539\u8b8a\u5c40\u52e2\u3002\u8001\u5e2b\u63d0\u51fa\u4e00\u500b\u53ef\u80fd\u6027\uff1a\u52a0\u5165\u7269\u7a2eB\u6216\u7269\u7a2eC\u7684\u5929\u6575\u7269\u7a2eD\uff0c\u8b93\u7269\u7a2eD\u53bb\u58d3\u5236\u7269\u7a2eB\u6216\u7269\u7a2eC\u5176\u4e2d\u4e00\u65b9\u3002\u7269\u7a2eD\u58d3\u5236\u7684\u7d50\u679c\uff0c\u53cd\u800c\u9020\u5c31\u7269\u7a2eB\u548c\u7269\u7a2eC\u5f97\u4ee5\u5171\u5b58\u3002<\/p>\n<p>&nbsp;<\/p>\n<p>\u6700\u5f8c\uff0c\u7dad\u4e2d\u8001\u5e2b\u66ff\u4e0a\u8ff0\u7684\u7814\u7a76\u65b9\u6cd5\u505a\u4e00\u500b\u6b78\u7d50\u3002\u6211\u5011\u53ef\u4ee5\u5ef6\u4f38\u4eca\u5929\u6240\u770b\u5230\u7684\u6a21\u578b\uff0c\u6a21\u64ec\u81ea\u7136\u754c\u4e2d\u8907\u96dc\u7684\u98df\u6027\u95dc\u4fc2\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u8ab0\u662f\u91cd\u8981\u7684\u7269\u7a2e\uff1f<\/b><\/p>\n<p>\u6211\u5011\u5229\u7528\u4e0d\u540c\u7684\u4e2d\u5fc3\u6027\u6307\u6a19[3]\u4f86\u9032\u884c\u6392\u884c\uff1a\u300c\u901a\u5e38\u91cd\u8981\u7684\u7269\u7a2e\u4e0d\u7b49\u65bc\u662f\u7a00\u6709\u7269\u7a2e\u3002\u300d\u9019\u6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centrality\uff09\u548c\u7269\u7a2e\u7db2\u8def\u4f4d\u7f6e\u7684\u7368\u7279\u6027\uff08species positional uniqueness\uff09\uff0c\u61c9\u8a72\u662f\u8ca0\u76f8\u95dc\u7684\u3002<\/p>\n<p>&nbsp;<\/p>\n<p><b>\u8907\u96dc\u7684\u98df\u7269\u7db2\u80cc\u5f8c\u662f\u5426\u6709\u7c21\u55ae\u7684\u751f\u6210\u6a5f\u5236\uff1f<\/b><\/p>\n<p>\u300c\u690d\u7269\u5438\u6536\u967d\u5149\uff0c\u8b8a\u6210\u8349\u98df\u6027\u52d5\u7269\u7684\u98df\u7269\uff0c\u8349\u98df\u6027\u52d5\u7269\u53c8\u662f\u8089\u98df\u6027\u52d5\u7269\u7684\u98df\u7269\u2026\u2026\u3002\u300d\u8001\u5e2b\u5229\u7528\u9019\u5247\u60f3\u6cd5\uff0c\u4f86\u9032\u884c\u6a21\u64ec\u3002\u7cfb\u7d71\u4e2d\u6709R\u500b\u672a\u4f7f\u7528\u7684\u8cc7\u6e90\uff08\u98df\u6027\u4f4d\u968e0\uff09\uff0cN\u500b\u7269\u7a2e\u5c07\u6703\u51fa\u73fe\uff08\u751f\u614b\u7cfb\u4e2d\u8d77\u59cb\u72c0\u614b\u6c92\u6709\u4efb\u4f55\u751f\u7269\uff09\u3002<\/p>\n<p>\u96a8\u8457N\u548cR\u7684\u589e\u52a0\uff0c\u5c31\u6703\u7522\u751f\u300c\u8907\u96dc\u300d\u7684\u98df\u7269\u7db2\u3002\u4e4d\u770b\u4e4b\u4e0b\u5f88\u50cf\u73fe\u5be6\u4e16\u754c\u7684\u98df\u7269\u7db2\u3002\u56e0\u6b64\uff0c\u8001\u5e2b\u5c31\u4f7f\u7528\u4e2d\u8208\u5927\u5b78\u6797\u5e78\u52a9\u8001\u5e2b\u6240\u63d0\u4f9b\uff0c\u6838\u4e8c\u5ee0\u570b\u52dd\u7063\u7684\u7530\u91ce\u8abf\u67e5\u6578\u64da\u4f86\u9032\u884c\u61c9\u8b49\u3002\u8a72\u98df\u7269\u7db2\u7269\u7a2e\u4e4b\u9593\u7684\u98df\u6027\u95dc\u4fc2\u670936\u500b\u9023\u7d50\uff0c\u800c\u98df\u6027\u4f4d\u968e\u7684\u5c64\u7d1a\u6578\u70ba8\u3002<\/p>\n<p>\u4ee4\u4eba\u50b7\u5fc3\u5730\u767c\u73fe\uff0c\u98df\u6027\u95dc\u4fc2\u6578\u6700\u9ad8\u53ea\u80fd\u6a21\u64ec\u523028\u3002\u800c\u98df\u6027\u4f4d\u968e\u7684\u5c64\u7d1a\u6578\u96d6\u7136\u53ef\u4ee5\u52308\uff0c\u4f46\u662f\u7576\u5c64\u7d1a\u6578\u70ba8\u6642\uff0c\u98df\u6027\u95dc\u4fc2\u6578\u76ee\u537b\u76f8\u7576\u7684\u4f4e\u3002<\/p>\n<p>\u8001\u5e2b\u79c9\u6301\u7814\u7a76\u8005\u7684\u7cbe\u795e\uff0c\u52a0\u5165\u300c\u99ac\u592a\u6548\u61c9\u300d\u7684\u5047\u8a2d\uff1a\u300c\u5927\u8005\u6046\u5927\u3002\u300d\u4e5f\u5c31\u662f\uff1a\u4e00\u500b\u6709\u8f03\u591a\u8cc7\u6e90\u7684\u7269\u7a2e\uff0c\u6703\u6709\u66f4\u591a\u7d93\u9a57\u627e\u66f4\u591a\u7684\u8cc7\u6e90\u3002\u53ef\u60dc\u7d50\u679c\u4e26\u4e0d\u5982\u9810\u671f\u3002<\/p>\n<p>\u7814\u7a76\u7684\u8def\u9014\u662f\u8981\u6108\u632b\u6108\u52c7\u7684\u3002\u5f9e\u53e6\u4e00\u500b\u89d2\u5ea6\u5207\u5165\uff0c\u8001\u5e2b\u6539\u63a1\u300c\u4f7f\u7528\u6548\u61c9\u300d\u7684\u5169\u500b\u5047\u60f3\u3002\u5047\u60f3\u4e00\uff1a\u6216\u8a31\u7269\u7a2e\u6bd4\u8f03\u559c\u6b61\u5403\u63a5\u8fd1\u4ed6\u5011\u98df\u6027\u4f4d\u968e\u7684\u98df\u7269\u3002\u4f8b\u5982\uff1a\u7345\u5b50\u6bd4\u8f03\u559c\u6b61\u5403\u725b\u7f8a\uff0c\u4e0d\u559c\u6b61\u5403\u6606\u87f2\u3002\u5047\u60f3\u4e8c\uff1a\u9ad8\u968e\u7269\u7a2e\u8f03\u6709\u79fb\u52d5\u80fd\u529b\uff0c\u6240\u4ee5\u8f03\u5bb9\u6613\u5230\u9054\u6211\u5011\u7684\u751f\u614b\u7cfb\u7d71\u3002\u56e0\u6b64\uff0c\u9ad8\u968e\u7684\u98df\u7269\u6703\u6bd4\u4f4e\u968e\u7684\u98df\u7269\u66f4\u5bb9\u6613\u88ab\u65b0\u4f86\u7684\u7269\u7a2e\u4f7f\u7528\u3002\u4e5f\u6210\u529f\u6a21\u64ec\u51fa\u570b\u52dd\u7063\u7684\u98df\u7269\u7db2\u6a21\u578b\u3002<\/p>\n<p>\u300c\u99ac\u592a\u6548\u61c9\u300d\uff0c\u662f\u8b93\u98df\u7269\u7db2\u671d\u6c34\u5e73\u65b9\u5411\u767c\u5c55\u7684\u6a5f\u5236\u3002\u800c\u300c\u4f7f\u7528\u6548\u61c9\u300d\uff0c\u662f\u8b93\u98df\u7269\u7db2\u671d\u8457\u5782\u76f4\u65b9\u5411\u767c\u5c55\u7684\u6a5f\u5236\u3002\u800c\u570b\u52dd\u7063\u751f\u614b\u7cfb\u7684\u767c\u5c55\u904e\u7a0b\uff0c\u5c31\u7531\u96fb\u8166\u6a21\u64ec\u8fb2\u5834\uff0c\u5f97\u77e5\u53ef\u80fd\u662f\u7531\u300c\u4f7f\u7528\u6548\u61c9\u300d\u800c\u975e\u300c\u99ac\u592a\u6548\u61c9\u300d\u6240\u7522\u751f\u3002<\/p>\n<p>&nbsp;<\/p>\n<div>\n<hr align=\"left\" size=\"1\" width=\"33%\" \/>\n<div>\n<p><a title=\"\" href=\"file:\/\/\/C:\/Users\/ntucase\/Downloads\/%5b%E7%89%B9%E7%A8%BF%5d%20%E7%8F%BE%E5%AF%A6%E7%94%9F%E6%B4%BB%E7%9A%84%E6%A8%A1%E6%93%AC%E8%BE%B2%E5%A0%B4--%E6%BC%AB%E8%AB%87%E7%94%9F%E6%85%8B%E7%B3%BB%E4%B8%AD%E7%9A%84%E6%97%8F%E7%BE%A4%E6%95%B8%E9%87%8F%E8%AE%8A%E5%8C%96.docx#_ftnref1\">[1]<\/a> \u5e73\u8861\u53ef\u4ee5\u5206\u6210\u5169\u985e\u3002\u7a69\u5b9a\uff08locally stable\uff09\u548c\u975e\u7a69\u5b9a\uff08locally unstable\uff09\u7a69\u5b9a\u7684\u5e73\u8861\u9ede\uff0c\u53ef\u4ee5\u7d93\u5f97\u8d77\u8f15\u5fae\u7684\u64fe\u52d5\u3002\u800c\u975e\u7a69\u5b9a\u7684\u5e73\u8861\u9ede\uff0c\u5c31\u6703\u7522\u751f\u9707\u76ea\u8207\u5931\u5e8f\u7684\u72c0\u614b\u3002<\/p>\n<\/div>\n<div>\n<p><a title=\"\" 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href=\"https:\/\/case.ntu.edu.tw\/CASTUDIO\/course.php?speech_ID=3475#video_top\" target=\"_blank\" rel=\"noopener noreferrer\">\u5168\u7a0b\u5f71\u97f3<\/a><\/p>\n<p><strong>\u8cac\u4efb\u7de8\u8f2f\uff1aVita Chen<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c\u4e03\u8b1b\u2027\u7279\u7a3f \u25a0 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