{"id":578,"date":"2026-07-16T14:58:34","date_gmt":"2026-07-16T06:58:34","guid":{"rendered":"https:\/\/arkdoc.cc\/?p=578"},"modified":"2026-07-16T16:22:52","modified_gmt":"2026-07-16T08:22:52","slug":"578","status":"publish","type":"post","link":"https:\/\/arkdoc.cc\/index.php\/2026\/07\/16\/578\/","title":{"rendered":""},"content":{"rendered":"\n <div id=\"preview\" class=\"latex-article tex2jax_process dark\">\n            <h1>Lecture: Global Dynamics<\/h1>\n<p>\u8fd9\u662f\u5e26\u6709\u4e00\u5f20\u79d1\u5b66\u56fe\u50cf\u5360\u4f4d\u7b26\u7684\u6bb5\u843d\u3002\u5728\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u4e66\u5199 <span style=\"color: red;\">\u5e26\u7ea2\u8272\u7684\u91cd\u70b9\u6587\u5b57<\/span>\uff0c\u6216\u8005\u4f7f\u7528\u7ecf\u5178\u7684 <span style=\"color: #16a34a;\">\u68ee\u6797\u7eff\u5341\u516d\u8fdb\u5236\u989c\u8272<\/span>\u3002<\/p>\n<p>\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528\u5927\u62ec\u53f7\u5199\u6cd5\uff1a<span style=\"color: #2f54eb;\">\u8fd9\u4e00\u6bb5\u6587\u5b57\u662f\u9ad8\u4eae\u7684\u4e3b\u9898\u84dd\u8272<\/span>\u3002<\/p>\n<div class=\"latex-figure\">  <div class=\"image-placeholder\">    <svg viewBox=\"0 0 24 24\"><path fill=\"currentColor\" d=\"M21 19V5c0-1.1-.9-2-2-2H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2zM8.5 13.5l2.5 3.01L14.5 12l4.5 6H5l3.5-4.5z\"\/><\/svg>    <span>\u56fe\u7247\u5360\u4f4d\u7b26<\/span>    <span class=\"image-filename\">convergence_analysis.png<\/span>  <\/div>  <div class=\"figure-caption\">\u56fe: \u7cfb\u7edf\u7684\u72b6\u6001\u8f68\u8ff9\u6536\u655b\u884c\u4e3a (Convergence Curve)<\/div><\/div>\n<p>\u8fd9\u91cc\u8fd8\u6709\u4e00\u5f20\u4e09\u7ebf\u5b66\u672f\u62a5\u8868\uff0c\u5c55\u793a\u4e86\u4e0d\u540c\u7cfb\u7edf\u53c2\u6570\u4e0b\u7684\u8bc4\u4f30\u6570\u636e\uff1a<\/p>\n<div class=\"latex-table-container\">  <div class=\"table-caption\">\u8868: \u5168\u5c40\u52a8\u6001\u7cfb\u7edf\u7684\u8fd0\u884c\u6548\u7387\u5bf9\u6bd4<\/div>  <table class=\"latex-table\"><tr><td>\u65b9\u6848\u7c7b\u578b<\/td><td>\u8fed\u4ee3\u6b65\u6570 (Iterations)<\/td><td>\u6536\u655b\u6b8b\u5dee<\/td><\/tr><tr><td>\u53e4\u5178 Euler<\/td><td>1200<\/td><td>$1.2 \\times 10^{-5}$<\/td><\/tr><tr><td>\u56db\u9636 Runge-Kutta<\/td><td>120<\/td><td>$3.4 \\times 10^{-12}$<\/td><\/tr><tr><td>\u8f9b\u8c31\u79ef\u5206\u5668<\/td><td>85<\/td><td>$9.1 \\times 10^{-15}$<\/td><\/tr><\/table><\/div>\n<p class=\"no-indent-p\">\u6240\u6709\u7684\u516c\u5f0f\u548c\u666e\u901a\u6bb5\u843d\u6392\u7248\u4f9d\u7136\u80fd\u6b63\u5e38\u914d\u5408\u6e32\u67d3\uff01<\/p>\n<p class=\"no-indent-p\">\u8fd9\u662f\u4e00\u4e2a\u4f7f\u7528\u4e86 \u5e76\u4e14\u5e26\u6709\u7279\u6b8a\u7a7a\u683c\u7684\u6bb5\u843d\uff1a\n$\\dot{x}_i = x_i (r_i &#8211; a_i x_i)$<\/p>\n<p class=\"no-indent-p\">\u5373\u4f7f\u8fd9\u91cc\u7d27\u8ddf\u5728\u516c\u5f0f\u540e\u65b9\uff0c\u53ea\u8981\u5e26\u6709 \u547d\u4ee4\uff0c\u5b83\u5c31\u4e0d\u4f1a\u4ea7\u751f\u4efb\u4f55\u7f29\u8fdb\u3002<\/p>\n<p>\u8fd9\u662f\u4e00\u4e2a\u6b63\u5e38\u7684\u6bb5\u843d\uff0c\u4f60\u4f1a\u53d1\u73b0\u5b83\u5177\u5907\u9ed8\u8ba4\u7684 2em \u5b66\u672f\u7f29\u8fdb\u3002\u5728\u6bb5\u843d\u4e2d\u6211\u4eec\u53ef\u4ee5\u65e0\u7f1d\u5d4c\u5957\u50cf <em>\u5f3a\u8c03\uff08emph\uff09<\/em> \u6216\u8005\u662f\u5927\u62ec\u53f7\u7ea7\u8054\u7684 <em>\u7ecf\u5178\u659c\u4f53<\/em>\u3002<\/p>\n<ul><li>\u68c0\u67e5\u65e0\u5e8f\u5217\u8868\u4e2d\u7684\u516c\u5f0f\uff1a${\\color{#2f54eb}\\frac{\\partial x}{\\partial t}=f_i(t,x) \\ge 0}$\u3002<\/li><li>\u53e6\u4e00\u4e2a\u5217\u8868\u9879\u3002<\/li><\/ul>\n\n        <\/div>\n    <\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Lecture: Global Dynamics \u8fd9\u662f\u5e26\u6709\u4e00\u5f20\u79d1\u5b66\u56fe\u50cf\u5360\u4f4d\u7b26\u7684\u6bb5\u843d\u3002\u5728\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u4e66\u5199 \u5e26\u7ea2\u8272 &hellip; <a href=\"https:\/\/arkdoc.cc\/index.php\/2026\/07\/16\/578\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\"><\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-578","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/posts\/578","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/comments?post=578"}],"version-history":[{"count":4,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/posts\/578\/revisions"}],"predecessor-version":[{"id":586,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/posts\/578\/revisions\/586"}],"wp:attachment":[{"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/media?parent=578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/categories?post=578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/arkdoc.cc\/index.php\/wp-json\/wp\/v2\/tags?post=578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}