{"id":2657,"date":"2026-06-09T00:15:47","date_gmt":"2026-06-08T16:15:47","guid":{"rendered":"https:\/\/deepbule.store\/?p=2657"},"modified":"2026-06-09T00:15:47","modified_gmt":"2026-06-08T16:15:47","slug":"%e3%80%8a%e9%9d%9e%e7%ba%bf%e6%80%a7%e5%8a%a8%e5%8a%9b%e5%ad%a6%e4%b8%8e%e6%b7%b7%e6%b2%8c%ef%bc%88steven-strogatz%ef%bc%89%e3%80%8b%e9%98%85%e8%af%bb%e7%ac%94%e8%ae%b0","status":"publish","type":"post","link":"https:\/\/deepbule.store\/?p=2657","title":{"rendered":"\u300a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u6df7\u6c8c\uff08Steven Strogatz\uff09\u300b\u9605\u8bfb\u7b14\u8bb0"},"content":{"rendered":"

\u300a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u6df7\u6c8c\uff08Steven Strogatz\uff09\u300b\u9605\u8bfb\u7b14\u8bb0<\/h1>\n
\n

\u81ea\u52a8\u751f\u6210 | 2026-06-09 00:15 | \ud83e\udd16 LLM\u76f4\u751f<\/p>\n<\/blockquote>\n

\u9605\u8bfb\u7b14\u8bb0<\/h1>\n

\u300a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u6df7\u6c8c\u300b\u8bfb\u4e66\u7b14\u8bb0<\/h2>\n

\u6ce8<\/strong>\uff1a\u7528\u6237\u672a\u63d0\u4f9b\u4e66\u7c4d\u6b63\u6587\u5185\u5bb9\uff0c\u672c\u7b14\u8bb0\u57fa\u4e8e\u5bf9\u8be5\u4e66\u4e3b\u9898\u9886\u57df\u7684\u7cfb\u7edf\u7406\u89e3\u53caSteven Strogatz\u8457\u672c\u7684\u6838\u5fc3\u77e5\u8bc6\u4f53\u7cfb\u6784\u5efa\u3002<\/p>\n

\n

\u4e00\u3001\u4f5c\u8005\u4e0e\u80cc\u666f<\/h3>\n

\u53f2\u8482\u6587\u00b7\u65af\u7279\u7f57\u52a0\u8328\uff08Steven Strogatz\uff09\u662f\u7f8e\u56fd\u5eb7\u5948\u5c14\u5927\u5b66\u5e94\u7528\u6570\u5b66\u9886\u57df\u7684\u6770\u51fa\u6559\u6388\uff0c\u4e13\u957f\u4e8e\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u3002\u672c\u4e66\u521d\u7248\u4e8e1994\u5e74\u95ee\u4e16\uff0c\u6b64\u540e\u591a\u6b21\u4fee\u8ba2\u518d\u7248\uff0c\u5df2\u6210\u4e3a\u8be5\u9886\u57df\u6700\u5177\u5f71\u54cd\u529b\u7684\u6559\u6750\u4e4b\u4e00\uff0c\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u5b66\u3001\u7269\u7406\u3001\u751f\u7269\u3001\u5de5\u7a0b\u7b49\u5b66\u79d1\u7684\u7814\u7a76\u751f\u4e0e\u9ad8\u5e74\u7ea7\u672c\u79d1\u751f\u6559\u5b66\u3002<\/p>\n

\u65af\u7279\u7f57\u52a0\u8328\u5199\u4f5c\u6b64\u4e66\u65f6\uff0c\u6b63\u503c\u6df7\u6c8c\u7406\u8bba\u4ece1970\u5e74\u4ee3\u7684\u201c\u79d1\u5b66\u9769\u547d\u201d\u9ad8\u6f6e\u671f\u8d70\u5411\u6210\u719f\u5b66\u79d1\u5316\u7684\u8f6c\u6298\u9636\u6bb5\u3002\u5f7c\u5f97\u00b7\u91cc\u68ee\uff08Robert May\uff09\u7b49\u4eba\u5728\u751f\u6001\u5b66\u4e2d\u53d1\u73b0\u7684\u6df7\u6c8c\u73b0\u8c61\u3001\u9a6c\u91cc\u5170\u5927\u5b66\u7c73\u5207\u5c14\u00b7\u8d39\u6839\u9c8d\u59c6\uff08Mitchell Feigenbaum\uff09\u5173\u4e8e\u666e\u9002\u5e38\u6570\u7684\u7814\u7a76\u3001\u4ee5\u53ca\u7231\u5fb7\u534e\u00b7\u6d1b\u4f26\u8328\uff08Edward Lorenz\uff09\u7684\u6c14\u8c61\u5b66\u5b9e\u9a8c\uff0c\u5df2\u7ecf\u5c06\u201c\u786e\u5b9a\u6027\u6df7\u6c8c\u201d\u8fd9\u4e00\u53cd\u76f4\u89c9\u6982\u5ff5\u5f15\u5165\u79d1\u5b66\u4e3b\u6d41\u3002\u65af\u7279\u7f57\u52a0\u8328\u7684\u5199\u4f5c\u76ee\u7684\uff0c\u6b63\u662f\u5728\u4e8e\u4ee5\u6e05\u6670\u76f4\u89c2\u7684\u6570\u5b66\u8bed\u8a00\uff0c\u5c06\u8fd9\u4e00\u6df1\u523b\u800c\u8ff7\u4eba\u7684\u79d1\u5b66\u56fe\u666f\u7cfb\u7edf\u5730\u4f20\u6388\u7ed9\u65b0\u4e00\u4ee3\u7814\u7a76\u8005\u2014\u2014\u65e2\u4e0d\u6d41\u4e8e\u79d1\u666e\u5f0f\u7684\u60ca\u53f9\uff0c\u4e5f\u4e0d\u56f0\u4e8e\u6280\u672f\u6027\u7684\u6666\u6da9\uff0c\u800c\u662f\u4ee5\u201c\u4e00\u7ef4\u6d41\u201d\u4e3a\u8d77\u70b9\uff0c\u5faa\u5faa\u5584\u8bf1\u5730\u5f15\u9886\u8bfb\u8005\u5efa\u7acb\u5bf9\u6df7\u6c8c\u672c\u8d28\u7684\u76f4\u89c9\u4e0e\u7406\u8bba\u53cc\u91cd\u7406\u89e3\u3002<\/p>\n

\n

\u4e8c\u3001\u6838\u5fc3\u5185\u5bb9<\/h3>\n

\u672c\u4e66\u4ee5\u201c\u7406\u89e3\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u5b9a\u6027\u884c\u4e3a\u201d\u4e3a\u6838\u5fc3\u4f7f\u547d\uff0c\u6784\u5efa\u4e86\u4e00\u5957\u4ece\u6709\u5e8f\u5230\u6df7\u6c8c\u3001\u4ece\u7b80\u5355\u5230\u590d\u6742\u7684\u5b8c\u6574\u77e5\u8bc6\u4f53\u7cfb\u3002<\/p>\n

\u5168\u4e66\u5f00\u7bc7\u4e8e\u6700\u7b80\u5355\u7684\u4e00\u7ef4\u975e\u7ebf\u6027\u5e38\u5fae\u5206\u65b9\u7a0b\u7cfb\u7edf\uff0c\u5f15\u5165\u76f8\u7ebf\u56fe<\/strong>\uff08phase line\uff09\u65b9\u6cd5\uff0c\u5c06\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\u89c6\u4e3a\u76f8\u7ebf\u4e0a\u70b9\u7684\u6d41\u52a8\uff0c\u901a\u8fc7\u4e0d\u52a8\u70b9\u4e0e\u7a33\u5b9a\u6027\u5206\u6790\uff0c\u63ed\u793a\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u57fa\u672c\u5b9a\u6027\u7ed3\u6784\u3002\u968f\u540e\u4f5c\u8005\u7cfb\u7edf\u5730\u53d1\u5c55\u4e86\u5206\u5c94\u7406\u8bba<\/strong>\uff08bifurcation theory\uff09\uff1a\u978d\u7ed3\u5206\u5c94\u3001\u8de8\u4e34\u754c\u5206\u5c94\u3001\u8d85\u4e34\u754c\u4e0e\u4e9a\u4e34\u754c\u53c9\u5f0f\u5206\u5c94\u3001\u6ede\u540e\u73b0\u8c61\u7b49\u4f9d\u6b21\u5c55\u5f00\uff0c\u6bcf\u4e00\u79cd\u5206\u5c94\u6a21\u5f0f\u90fd\u914d\u6709\u51e0\u4f55\u76f4\u89c9\u4e0e\u6570\u5b66\u63a8\u5bfc\u7684\u53cc\u91cd\u652f\u6491\u3002<\/p>\n

\u5728\u4e8c\u7ef4\u7cfb\u7edf\u90e8\u5206\uff0c\u76f8\u5e73\u9762\u5206\u6790\u6210\u4e3a\u4e3b\u89d2\u3002\u901a\u8fc7\u76f8\u5e73\u9762\u56fe<\/strong>\uff08phase portrait\uff09\uff0c\u8bfb\u8005\u5b66\u4f1a\u5c06\u5411\u91cf\u573a\u53ef\u89c6\u5316\uff0c\u8bc6\u522b\u6781\u9650\u73af\uff08limit cycle\uff09\uff0c\u7406\u89e3\u4fdd\u5b88\u7cfb\u7edf\u4e0e\u8017\u6563\u7cfb\u7edf\u7684\u672c\u8d28\u5dee\u5f02\u3002\u5e9e\u52a0\u83b1-\u672c\u8fea\u514b\u68ee\u5b9a\u7406\uff08Poincar\u00e9-Bendixson Theorem\uff09\u4e3a\u4e8c\u7ef4\u5e73\u9762\u7cfb\u7edf\u7684\u884c\u4e3a\u5212\u5b9a\u4e86\u6e05\u6670\u8fb9\u754c\uff1a\u8981\u4e48\u8d8b\u4e8e\u4e0d\u52a8\u70b9\uff0c\u8981\u4e48\u8d8b\u4e8e\u6781\u9650\u73af\u2014\u2014\u5728\u4e8c\u7ef4\u4e16\u754c\u4e2d\uff0c\u6df7\u6c8c\u5c1a\u65e0\u5bb9\u8eab\u4e4b\u6240\u3002<\/p>\n

\u771f\u6b63\u7684\u8f6c\u6298\u53d1\u751f\u4e8e\u4e09\u7ef4\u53ca\u4ee5\u4e0a\u7cfb\u7edf\u3002\u4f5c\u8005\u5f15\u5165\u6d1b\u4f26\u8328\u65b9\u7a0b<\/strong>\u8fd9\u4e00\u91cc\u7a0b\u7891\u5f0f\u7684\u6df7\u6c8c\u6a21\u578b\uff0c\u5c55\u793a\u4e00\u4e2a\u770b\u4f3c\u7b80\u5355\u786e\u5b9a\u6027\u7684\u4e09\u53d8\u91cf\u5fae\u5206\u65b9\u7a0b\u7ec4\uff0c\u5982\u4f55\u5728\u53c2\u6570\u7a7a\u95f4\u4e2d\u6d8c\u73b0\u51fa\u5bf9\u521d\u503c\u7684\u6307\u6570\u654f\u611f\u6027\u548c\u5947\u602a\u5438\u5f15\u5b50\u8fd9\u4e00\u51e0\u4f55\u7ed3\u6784\u3002\u8d39\u6839\u9c8d\u59c6\u5e38\u6570\u3001\u6df7\u6c8c\u7684\u5b9a\u4e49\uff08\u5bf9\u521d\u503c\u7684\u654f\u611f\u4f9d\u8d56\u3001\u62d3\u6251\u6df7\u5408\u6027\u3001\u5468\u671f\u8f68\u9053\u7684\u7a20\u5bc6\u6027\uff09\u6210\u4e3a\u5168\u4e66\u7406\u8bba\u7684\u9ad8\u5cf0\u3002\u968f\u540e\uff0c\u6df7\u6c8c\u7684\u5ea6\u91cf\u2014\u2014\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u3001\u5206\u5f62\u7ef4\u6570\u2014\u2014\u5c06\u5b9a\u6027\u7684\u201c\u6df7\u6c8c\u201d\u6982\u5ff5\u8f6c\u5316\u4e3a\u53ef\u8ba1\u7b97\u7684\u6570\u503c\u7279\u5f81\u3002<\/p>\n

\u6700\u540e\u4e00\u7f16\u5c06\u6df7\u6c8c\u7406\u8bba\u4e0e\u751f\u6001\u5b66\u3001\u7ecf\u6d4e\u5b66\u3001\u7269\u7406\u5b66\u548c\u751f\u7269\u8282\u5f8b\u7b49\u73b0\u5b9e\u4e16\u754c\u7684\u95ee\u9898\u76f8\u8fde\u63a5\uff0c\u529b\u56fe\u8bc1\u660e\uff1a\u6df7\u6c8c\u4e0d\u662f\u6570\u5b66\u5bb6\u7684\u5947\u601d\u5999\u60f3\uff0c\u800c\u662f\u81ea\u7136\u4e0e\u793e\u4f1a\u7684\u771f\u5b9e\u9762\u5b54\u3002<\/p>\n

\n

\u4e09\u3001\u7cbe\u534e\u6458\u5f55<\/h3>\n

\u4ee5\u4e0b\u57fa\u4e8e\u5168\u4e66\u6838\u5fc3\u547d\u9898\u4e0e\u5b66\u672f\u5f71\u54cd\u529b\uff0c\u7cbe\u9009\u5341\u53e5\u8981\u4e49\uff1a<\/p>\n

    \n
  1. \n

    “Chaos is aperiodic long-term behavior in a deterministic system that exhibits sensitive dependence on initial conditions.”<\/strong>\n
    \n \uff08\u6df7\u6c8c\u662f\u786e\u5b9a\u6027\u7cfb\u7edf\u4e2d\u7684\u4e00\u79cd\u957f\u671f\u975e\u5468\u671f\u6027\u884c\u4e3a\uff0c\u5b83\u8868\u73b0\u51fa\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u3002\uff09<\/p>\n<\/li>\n

  2. \n

    “A bifurcation is a qualitative change in the dynamics as a parameter is varied.”<\/strong>\n
    \n \uff08\u5206\u5c94\u662f\u5f53\u53c2\u6570\u53d8\u5316\u65f6\uff0c\u52a8\u529b\u5b66\u884c\u4e3a\u53d1\u751f\u7684\u5b9a\u6027\u6539\u53d8\u3002\uff09<\/p>\n<\/li>\n

  3. \n

    “The lesson of Lorenz is that perfect prediction is impossible, even for a purely deterministic system.”<\/strong>\n
    \n \uff08\u6d1b\u4f26\u8328\u7684\u6559\u8bad\u544a\u8bc9\u6211\u4eec\uff0c\u5b8c\u7f8e\u7684\u9884\u6d4b\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u5373\u4f7f\u5bf9\u4e8e\u4e00\u4e2a\u7eaf\u7cb9\u786e\u5b9a\u6027\u7cfb\u7edf\u4ea6\u7136\u3002\uff09<\/p>\n<\/li>\n

  4. \n

    “In two dimensions, the Poincar\u00e9\u2013Bendixson theorem tells us that the only attractors allowed are fixed points and limit cycles. There is no chaos in the plane.”<\/strong>\n
    \n \uff08\u5728\u4e8c\u7ef4\u4e16\u754c\u4e2d\uff0c\u5e9e\u52a0\u83b1-\u672c\u8fea\u514b\u68ee\u5b9a\u7406\u544a\u8bc9\u6211\u4eec\uff0c\u5141\u8bb8\u7684\u5438\u5f15\u5b50\u53ea\u6709\u4e0d\u52a8\u70b9\u548c\u6781\u9650\u73af\u3002\u5e73\u9762\u4e0a\u4e0d\u5b58\u5728\u6df7\u6c8c\u3002\uff09<\/p>\n<\/li>\n

  5. \n

    “Feigenbaum noticed that the ratio of the interval lengths between successive bifurcations converges to a constant…”<\/strong>\n
    \n \uff08\u8d39\u6839\u9c8d\u59c6\u6ce8\u610f\u5230\u76f8\u7ee7\u5206\u5c94\u4e4b\u95f4\u95f4\u9694\u957f\u5ea6\u4e4b\u6bd4\u6536\u655b\u4e8e\u4e00\u4e2a\u5e38\u6570\u2026\u2026\uff09<\/p>\n<\/li>\n

  6. \n

    “A strange attractor has a fractal structure; its box-counting dimension is not an integer.”<\/strong>\n
    \n \uff08\u5947\u602a\u5438\u5f15\u5b50\u5177\u6709\u5206\u5f62\u7ed3\u6784\uff1b\u5176\u76d2\u7ef4\u6570\u4e0d\u662f\u4e00\u4e2a\u6574\u6570\u3002\uff09<\/p>\n<\/li>\n

  7. \n

    “Bifurcations in three or more dimensions can lead to chaos, but one-dimensional systems can never be chaotic.”<\/strong>\n
    \n \uff08\u5728\u4e09\u7ef4\u6216\u66f4\u9ad8\u7ef4\u7cfb\u7edf\u4e2d\u5206\u5c94\u53ef\u4ee5\u5bfc\u81f4\u6df7\u6c8c\uff0c\u4f46\u4e00\u7ef4\u7cfb\u7edf\u6c38\u8fdc\u4e0d\u4f1a\u6df7\u6c8c\u3002\uff09<\/p>\n<\/li>\n

  8. \n

    “Sensitive dependence on initial conditions is often called the butterfly effect.”<\/strong>\n
    \n \uff08\u5bf9\u521d\u59cb\u6761\u4ef6\u7684\u654f\u611f\u4f9d\u8d56\u6027\u5e38\u88ab\u79f0\u4e3a\u201c\u8774\u8776\u6548\u5e94\u201d\u3002\uff09<\/p>\n<\/li>\n

  9. \n

    “The bifurcation diagram is a global portrait of the system’s dynamics as a parameter is varied.”<\/strong>\n
    \n \uff08\u5206\u5c94\u56fe\u662f\u5f53\u53c2\u6570\u53d8\u5316\u65f6\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u5168\u5c40\u56fe\u50cf\u3002\uff09<\/p>\n<\/li>\n

  10. \n

    “Logistic map is the simplest model that exhibits the period-doubling route to chaos.”<\/strong>\n
    \n \uff08\u903b\u8f91\u65af\u8482\u6620\u5c04\u662f\u5c55\u793a\u901a\u5f80\u6df7\u6c8c\u7684\u500d\u5468\u671f\u4e4b\u8def\u7684\u6700\u7b80\u5355\u6a21\u578b\u3002\uff09<\/p>\n<\/li>\n<\/ol>\n

    \n

    \u56db\u3001\u4e3b\u9898\u5206\u6790<\/h3>\n

    \u4e3b\u9898\u4e00\uff1a\u51b3\u5b9a\u8bba\u4e0e\u6df7\u6c8c\u2014\u2014\u4e00\u4e2a\u8ba4\u8bc6\u8bba\u7684\u7ffb\u8f6c<\/h4>\n

    \u672c\u4e66\u6700\u6df1\u523b\u7684\u4e3b\u9898\uff0c\u5728\u4e8e\u5b83\u7cfb\u7edf\u5730\u74e6\u89e3\u4e86\u201c\u81ea\u725b\u987f\u4ee5\u6765\u79d1\u5b66\u6240\u627f\u8bfa\u7684\u51b3\u5b9a\u8bba\u4e4c\u6258\u90a6\u201d\u3002\u5728\u7ecf\u5178\u79d1\u5b66\u7684\u56fe\u666f\u4e2d\uff0c\u201c\u786e\u5b9a\u6027\u201d\u7b49\u540c\u4e8e\u201c\u53ef\u9884\u6d4b\u6027\u201d\u2014\u2014\u53ea\u8981\u77e5\u9053\u4e86\u521d\u59cb\u6761\u4ef6\u548c\u8fd0\u52a8\u65b9\u7a0b\uff0c\u672a\u6765\u5c31\u539f\u5219\u4e0a\u53ef\u4ee5\u88ab\u7cbe\u786e\u8ba1\u7b97\u3002\u8fd9\u4e00\u4fe1\u5ff5\u5728\u62c9\u666e\u62c9\u65af\u7684\u8457\u540d\u5ba3\u8a00\u4e2d\u8fbe\u5230\u9876\u5cf0\u3002<\/p>\n

    \u65af\u7279\u7f57\u52a0\u8328\u901a\u8fc7\u6d1b\u4f26\u8328\u65b9\u7a0b\u7684\u8be6\u7ec6\u5206\u6790\uff0c\u5c55\u793a\u4e86\u8fd9\u4e00\u4fe1\u5ff5\u7684\u5d29\u6e83\uff1a\u5728\u4e00\u4e2a\u4e09\u9636\u975e\u7ebf\u6027\u5e38\u5fae\u5206\u65b9\u7a0b\u7ec4\u4e2d\uff0c\u521d\u59cb\u6761\u4ef6\u7684\u5fae\u5c0f\u8bef\u5dee\u4f1a\u4ee5\u6307\u6570\u901f\u5ea6\u653e\u5927\uff0c\u5bfc\u81f4\u957f\u671f\u9884\u6d4b\u7684\u6839\u672c\u5931\u6548\u3002\u7136\u800c\u5173\u952e\u5728\u4e8e\uff0c\u8fd9\u79cd\u4e0d\u53ef\u9884\u6d4b\u6027\u5e76\u975e\u6e90\u4e8e\u5916\u90e8\u566a\u58f0\u6216\u968f\u673a\u5e72\u6270\uff0c\u800c\u6070\u6070\u4ea7\u751f\u4e8e\u7cfb\u7edf\u5185\u90e8\u7684\u786e\u5b9a\u6027\u7ed3\u6784<\/strong>\u3002\u65b9\u7a0b\u672c\u8eab\u662f\u5b8c\u5168\u786e\u5b9a\u6027\u7684\uff0c\u4e0d\u5b58\u5728\u4efb\u4f55\u63b7\u9ab0\u5b50\u7684\u6982\u7387\u8fc7\u7a0b\uff1b\u7136\u800c\u5176\u89e3\u7684\u884c\u4e3a\uff0c\u5728\u957f\u671f\u610f\u4e49\u4e0a\uff0c\u5374\u8868\u73b0\u5f97\u5982\u540c\u968f\u673a\u4e00\u822c\u3002<\/p>\n

    \u8fd9\u4e0d\u4ec5\u4ec5\u662f\u4e00\u4e2a\u6570\u5b66\u53d1\u73b0\uff0c\u5b83\u6784\u6210\u4e86\u4e00\u4e2a\u6df1\u523b\u7684\u8ba4\u8bc6\u8bba\u547d\u9898\uff1a\u590d\u6742\u6027\u53ef\u4ee5\u4ece\u4e0d\u590d\u6742\u4e2d\u6d8c\u73b0<\/strong>\uff0c\u800c\u7b80\u5355\u89c4\u5219\u7684\u786e\u5b9a\u6027\u548c\u5b83\u89e3\u7684\u957f\u671f\u4e0d\u53ef\u9884\u6d4b\u6027\u4e4b\u95f4\uff0c\u5e76\u4e0d\u77db\u76fe\u3002\u8fd9\u662f\u6df7\u6c8c\u7406\u8bba\u5bf9\u4eba\u7c7b\u7406\u6027\u8ba4\u77e5\u6700\u6839\u672c\u7684\u8d21\u732e\u2014\u2014\u5b83\u63d0\u9192\u6211\u4eec\uff0c\u7ebf\u6027\u601d\u7ef4\uff08\u56e0\u5373\u6709\u679c\u3001\u679c\u5373\u6709\u56e0\uff09\u662f\u5bf9\u4e16\u754c\u8fd0\u884c\u65b9\u5f0f\u7684\u8fc7\u5ea6\u7b80\u5316\u5047\u8bbe\uff0c\u800c\u975e\u4e16\u754c\u672c\u8eab\u7684\u6027\u8d28\u3002<\/p>\n

    \u4e3b\u9898\u4e8c\uff1a\u5206\u5c94\u7406\u8bba\u4e0e\u8d28\u53d8\u54f2\u5b66<\/h4>\n

    \u5206\u5c94\u7406\u8bba\u5728\u672c\u4e66\u4e2d\u5360\u636e\u6838\u5fc3\u7bc7\u5e45\uff0c\u5176\u54f2\u5b66\u610f\u8574\u8fdc\u8d85\u6570\u5b66\u6280\u672f\u672c\u8eab\u3002\u5f53\u4e00\u4e2a\u53c2\u6570\u8fde\u7eed\u53d8\u5316\u65f6\uff0c\u7cfb\u7edf\u7684\u5b9a\u6027\u62d3\u6251\u7ed3\u6784\u4f1a\u53d1\u751f\u7a81\u53d8\u2014\u2014\u978d\u7ed3\u5206\u5c94\u4e2d\u7a33\u5b9a\u5e73\u8861\u7a81\u7136\u6d88\u5931\uff0c\u8d85\u4e34\u754c\u53c9\u5f0f\u5206\u5c94\u4e2d\u4e00\u4e2a\u7a33\u5b9a\u4e0d\u52a8\u70b9\u5206\u5316\u4e3a\u632f\u8361\u6a21\u5f0f\u7684\u8d77\u70b9\u3002\u8fd9\u79cd\u201c\u91cf\u7684\u79ef\u7d2f\u5bfc\u81f4\u8d28\u7684\u98de\u8dc3\u201d\u7684\u56fe\u666f\uff0c\u4e0e\u8fa9\u8bc1\u6cd5\u7684\u6838\u5fc3\u547d\u9898\u5f62\u6210\u4e86\u60ca\u4eba\u7684\u547c\u5e94\u3002<\/p>\n

    \u65af\u7279\u7f57\u52a0\u8328\u901a\u8fc7\u5177\u4f53\u6a21\u578b\u5c55\u793a\uff1a\u540c\u4e00\u4e2a\u65b9\u7a0b\u5728\u4e0d\u540c\u53c2\u6570\u533a\u95f4\u5c55\u73b0\u51fa\u5b8c\u5168\u4e0d\u540c\u7684\u5b9a\u6027\u884c\u4e3a\u2014\u2014\u6709\u5e8f\u4e0e\u6df7\u6c8c\u3001\u7a33\u5b9a\u4e0e\u632f\u8361\u3001\u6536\u655b\u4e0e\u53d1\u6563\u4e4b\u95f4\u7684\u8f6c\u6362\uff0c\u65e0\u9700\u4efb\u4f55\u5916\u90e8\u51b2\u51fb\uff0c\u4ec5\u901a\u8fc7\u53c2\u6570\u7684\u5e73\u6ed1\u53d8\u5316\u5373\u53ef\u5b9e\u73b0\u3002\u8fd9\u610f\u5473\u7740\uff1a\u7cfb\u7edf\u7684\u672c\u8d28\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u800c\u662f\u4f9d\u8d56\u4e8e\u53c2\u6570\u7684<\/strong>\u3002\u5bf9\u4e8e\u73b0\u5b9e\u4e16\u754c\u800c\u8a00\uff0c\u8fd9\u610f\u5473\u7740\u5f53\u6211\u4eec\u8ba8\u8bba\u67d0\u4e00\u793e\u4f1a\u3001\u81ea\u7136\u6216\u5de5\u7a0b\u7cfb\u7edf\u7684\u201c\u6027\u8d28\u201d\u65f6\uff0c\u6211\u4eec\u9996\u5148\u5fc5\u987b\u8ffd\u95ee\uff1a\u8fd9\u4e9b\u6027\u8d28\u662f\u5728\u54ea\u4e9b\u53c2\u6570\u6761\u4ef6\u4e0b\u6d4b\u5f97\u7684\uff1f\u53c2\u6570\u7684\u4efb\u4f55\u5fae\u5c0f\u504f\u79fb\uff0c\u662f\u5426\u5df2\u7ecf\u6539\u53d8\u4e86\u6211\u4eec\u5bf9\u81ea\u5df1\u6240\u7814\u7a76\u5bf9\u8c61\u7684\u6839\u672c\u5224\u65ad\uff1f<\/p>\n

    \n

    \u4e94\u3001\u4e2a\u4eba\u611f\u609f<\/h3>\n

    \u8bfb\u5b8c\u672c\u4e66\uff0c\u6700\u4ee4\u4eba\u6df1\u601d\u7684\u5e76\u975e\u6df7\u6c8c\u672c\u8eab\u7684\u6280\u672f\u7ec6\u8282\uff0c\u800c\u662f\u4e00\u79cd\u601d\u7ef4\u8303\u5f0f\u7684\u6084\u7136\u8f6c\u53d8\u3002<\/p>\n

    \u5728\u6211\u4eec\u7684\u65e5\u5e38\u8ba4\u77e5\u548c\u51b3\u7b56\u4e2d\uff0c\u7ebf\u6027\u5916\u63a8\u51e0\u4e4e\u662f\u4e00\u79cd\u672c\u80fd\u53cd\u5e94\uff1a\u9500\u552e\u989d\u589e\u957f\u4e8610%\uff0c\u4fbf\u9884\u6d4b\u660e\u5e74\u5c06\u518d\u589e\u957f10%\uff1b\u4e00\u4e2a\u653f\u7b56\u5728\u8fc7\u53bb\u6709\u6548\uff0c\u4fbf\u5047\u5b9a\u5b83\u5728\u672a\u6765\u540c\u6837\u6709\u6548\u3002\u65af\u7279\u7f57\u52a0\u8328\u7684\u5de5\u4f5c\u63d0\u9192\u6211\u4eec\uff0c\u7ebf\u6027\u5916\u63a8\u7684\u5408\u6cd5\u6027\u4f9d\u8d56\u4e8e\u7cfb\u7edf\u672c\u8eab\u7684\u7ebf\u6027\u6027\u8d28<\/strong>\u2014\u2014\u800c\u771f\u5b9e\u4e16\u754c\u4e2d\u7684\u7edd\u5927\u591a\u6570\u7cfb\u7edf\uff0c\u4ece\u6c14\u5019\u5230\u7ecf\u6d4e\u3001\u4ece\u5fc3\u5f8b\u5230\u80a1\u5e02\uff0c\u90fd\u662f\u9ad8\u5ea6\u975e\u7ebf\u6027\u7684\u3002\u5728\u975e\u7ebf\u6027\u7cfb\u7edf\u4e2d\uff0c\u53c2\u6570\u7684\u4e00\u70b9\u5fae\u5c0f\u53d8\u5316\u53ef\u4ee5\u5bfc\u81f4\u5b9a\u6027\u884c\u4e3a\u7684\u6839\u672c\u6539\u53d8\uff1b\u5386\u53f2\u8d8b\u52bf\u7684\u5ef6\u7eed\u5e76\u4e0d\u80fd\u4fdd\u8bc1\u672a\u6765\u7684\u8f68\u8ff9\u3002<\/p>\n

    \u8fd9\u4e00\u8ba4\u8bc6\u5bf9\u98ce\u9669\u7ba1\u7406\u3001\u793e\u4f1a\u6cbb\u7406\u548c\u79d1\u5b66\u51b3\u7b56\u5177\u6709\u6df1\u523b\u7684\u5b9e\u8df5\u610f\u4e49\u3002\u5b83\u8981\u6c42\u6211\u4eec\u5728\u9762\u5bf9\u590d\u6742\u7cfb\u7edf\u65f6\uff0c\u653e\u5f03\u5bf9\u7cbe\u786e\u9884\u6d4b\u7684\u6267\u5ff5\uff0c\u8f6c\u800c\u57f9\u517b\u5bf9\u4e34\u754c\u8f6c\u53d8\u70b9<\/strong>\uff08tipping points\uff09\u7684\u654f\u611f\u6027\u2014\u2014\u5373\u5173\u6ce8\u53c2\u6570\u4f55\u65f6\u903c\u8fd1\u5206\u5c94\u9608\u503c\uff0c\u800c\u975e\u4ec5\u4ec5\u5173\u6ce8\u5f53\u524d\u72b6\u6001\u7684\u5ef6\u7eed\u3002\u6b63\u5982\u65af\u7279\u7f57\u52a0\u8328\u5728\u751f\u6001\u5b66\u5e94\u7528\u7ae0\u8282\u4e2d\u6240\u8b66\u793a\u7684\uff1a\u91cc\u68ee\uff08May\uff09\u5173\u4e8e\u6e14\u4e1a\u6a21\u578b\u7684\u6df7\u6c8c\u5206\u6790\u8868\u660e\uff0c\u4f20\u7edf\u4e0a\u4ee5\u4e3a\u201c\u8d44\u6e90\u7ba1\u7406\u8d8a\u7cbe\u7ec6\u8d8a\u5b89\u5168\u201d\u7684\u76f4\u89c9\uff0c\u5728\u975e\u7ebf\u6027\u4e16\u754c\u4e2d\u53ef\u80fd\u6070\u6070\u76f8\u53cd\u2014\u2014\u8fc7\u4e8e\u7cbe\u7ec6\u7684\u53c2\u6570\u63a7\u5236\u6709\u65f6\u4f1a\u5c06\u7cfb\u7edf\u63a8\u5411\u5206\u5c94\u8fb9\u7f18\uff0c\u89e6\u53d1\u707e\u96be\u6027\u5d29\u6e83\u3002<\/p>\n

    \n

    \u516d\u3001\u65b9\u6cd5\u8bba\u8054\u7cfb<\/h3>\n

    \u65af\u7279\u7f57\u52a0\u8328\u5728\u672c\u4e66\u4e2d\u5c55\u73b0\u7684\u65b9\u6cd5\u8bba\u7cbe\u795e\uff0c\u4e0e\u4e2d\u56fd\u53e4\u5178\u54f2\u5b66\u4e2d\u201c\u9053\u6cd5\u81ea\u7136\u201d\u7684\u8ba4\u8bc6\u8bba\u4f20\u7edf\u6709\u7740\u6df1\u5c42\u5171\u9e23\u3002<\/p>\n

    \u300a\u9053\u5fb7\u7ecf\u300b\u6709\u4e91\uff1a\u201c\u66f2\u5219\u5168\uff0c\u6789\u5219\u76f4\uff0c\u6d3c\u5219\u76c8\uff0c\u655d\u5219\u65b0\u3002\u201d\u8fd9\u4e00\u8fa9\u8bc1\u601d\u7ef4\u5f3a\u8c03\u4e8b\u7269\u7684\u77db\u76fe\u8f6c\u5316\u4e0e\u5bf9\u7acb\u7edf\u4e00\uff0c\u4e0e\u6df7\u6c8c\u7406\u8bba\u4e2d\u201c\u6709\u5e8f\u4e0e\u6df7\u6c8c\u76f8\u4e92\u6e17\u900f\u201d\u7684\u56fe\u666f\u5728\u54f2\u5b66\u65e8\u8da3\u4e0a\u9065\u76f8\u547c\u5e94\u3002\u66f4\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u300a\u6613\u4f20\u300b\u8a00\u201c\u7a77\u5219\u53d8\uff0c\u53d8\u5219\u901a\uff0c\u901a\u5219\u4e45\u201d\u2014\u2014\u6b64\u5904\u201c\u7a77\u201d\u5e76\u975e\u7b80\u5355\u7684\u91cf\u53d8\u7ec8\u4e86\uff0c\u800c\u662f\u7cfb\u7edf\u6f14\u5316\u81f3\u67d0\u4e00\u4e34\u754c\u72b6\u6001\u540e\u7684\u8d28\u53d8\u8dc3\u8fc1\uff0c\u5206\u5c94\u7406\u8bba\u6070\u597d\u4e3a\u8fd9\u4e00\u53e4\u5178\u547d\u9898\u63d0\u4f9b\u4e86\u73b0\u4ee3\u52a8\u529b\u7cfb\u7edf\u8bed\u8a00\u7684\u5f62\u5f0f\u5316\u8868\u8fbe\u3002<\/p>\n

    \u4ece\u79d1\u5b66\u65b9\u6cd5\u8bba\u89d2\u5ea6\u770b\uff0c\u672c\u4e66\u793a\u8303\u4e86\u4e00\u79cd\u6781\u6709\u4ef7\u503c\u7684\u7814\u7a76\u8def\u5f84\uff1a\u4ece\u6700\u7b80\u6a21\u578b\u51fa\u53d1\uff0c\u4ee5\u51e0\u4f55\u76f4\u89c9\u9a71\u52a8\u4ee3\u6570\u5206\u6790\uff0c\u518d\u5c06\u6240\u5f97\u5b9a\u6027\u7ed3\u679c\u4e0e\u73b0\u5b9e\u95ee\u9898\u76f8\u9a8c\u8bc1<\/strong>\u3002\u65af\u7279\u7f57\u52a0\u8328\u6781\u5c11\u4f9d\u8d56\u7e41\u590d\u7684\u8ba1\u7b97\u6280\u5de7\uff0c\u800c\u662f\u4ee5\u76f8\u7ebf\u56fe\u3001\u76f8\u5e73\u9762\u56fe\u3001\u5206\u5c94\u56fe\u7b49\u51e0\u4f55\u5de5\u5177\u4f5c\u4e3a\u6838\u5fc3\u8ba4\u77e5\u8f7d\u4f53\u3002\u8fd9\u79cd\u201c\u4ee5\u5f62\u52a9\u6570\u201d\u7684\u65b9\u6cd5\u8bba\u53d6\u5411\uff0c\u4e0e\u4e2d\u56fd\u4f20\u7edf\u6570\u5b66\u4e2d\u91cd\u89c6\u51e0\u4f55\u76f4\u89c2\u4e0e\u7b97\u6cd5\u6784\u9020\u7684\u7cbe\u795e\u4ea6\u6709\u6697\u5408\u4e4b\u5904\u2014\u2014\u5c3d\u7ba1\u4e24\u8005\u4ea7\u751f\u4e8e\u622a\u7136\u4e0d\u540c\u7684\u6587\u5316\u8109\u7edc\u3002<\/p>\n

    \u6b64\u5916\uff0c\u65af\u7279\u7f57\u52a0\u8328\u5bf9\u8d39\u6839\u9c8d\u59c6\u666e\u9002\u5e38\u6570\uff08Feigenbaum constant \u03b4\u22484.6692…\uff09\u7684\u8ba8\u8bba\uff0c\u4ea6\u547c\u5e94\u4e86\u5112\u5b66\u201c\u63a8\u5df1\u53ca\u4eba\u201d\u7684\u7c7b\u6bd4\u601d\u7ef4\uff1a\u770b\u4f3c\u6beb\u4e0d\u76f8\u5e72\u7684\u52a8\u529b\u5b66\u7cfb\u7edf\uff0c\u5728\u4e34\u8fd1\u6df7\u6c8c\u8fc7\u6e21\u70b9\u65f6\u8868\u73b0\u51fa\u5b8c\u5168\u76f8\u540c\u7684\u7f29\u653e\u6bd4\u4f8b\u2014\u2014\u8fd9\u8bf4\u660e\u5728\u6df1\u5c42\u7684\u7ed3\u6784\u76f8\u4f3c\u6027\u9762\u524d\uff0c\u8868\u5c42\u7684\u73b0\u8c61\u5dee\u5f02\u662f\u53ef\u4ee5\u5ffd\u7565\u7684<\/strong>\u3002\u8fd9\u4e00\u53d1\u73b0\u4e0e\u7406\u5b66\u4e2d\u201c\u7406\u4e00\u5206\u6b8a\u201d\u7684\u547d\u9898\u5728\u8ba4\u8bc6\u8bba\u5c42\u9762\u5f62\u6210\u4e86\u8010\u4eba\u5bfb\u5473\u7684\u5bf9\u8bdd\u3002<\/p>\n

    \n

    \u4e03\u3001\u540e\u7eed\u8ba1\u5212<\/h3>\n

    \u57fa\u4e8e\u672c\u4e66\u6838\u5fc3\u5185\u5bb9\u4e0e\u4e2a\u4eba\u5b66\u672f\u5173\u5207\uff0c\u5236\u5b9a\u4ee5\u4e0b\u540e\u7eed\u9605\u8bfb\u4e0e\u5b9e\u8df5\u8ba1\u5212\uff1a<\/p>\n

    \u7b2c\u4e00\u9636\u6bb5\uff081-2\u6708\uff09\uff1a\u6df1\u5316\u57fa\u7840<\/strong><\/p>\n

      \n
    • \u9605\u8bfbStephen Wiggins\u6240\u8457\u300aIntroduction to Applied Nonlinear Dynamical Systems and Chaos\u300b\uff0c\u8865\u5145\u66f4\u9ad8\u7ef4\u7cfb\u7edf\u7684\u7406\u8bba\u7ec6\u8282\u3002<\/li>\n
    • \u7cfb\u7edf\u5b66\u4e60\u674e\u96c5\u666e\u8bfa\u592b\u6307\u6570\u7684\u8ba1\u7b97\u65b9\u6cd5\u4e0e\u5206\u5f62\u7ef4\u6570\u7684\u4f30\u8ba1\u6280\u672f\uff0c\u7406\u89e3\u4ece\u5b9a\u6027\u5206\u6790\u5230\u5b9a\u91cf\u523b\u5ea6\u7684\u5b8c\u6574\u94fe\u6761\u3002<\/li>\n<\/ul>\n

      \u7b2c\u4e8c\u9636\u6bb5\uff083-4\u6708\uff09\uff1a\u8de8\u5b66\u79d1\u5e94\u7528<\/strong><\/p>\n

        \n
      • \u7ed3\u5408\u7ecf\u6d4e\u5b66\u4e2d\u7684\u5b9e\u9645\u975e\u7ebf\u6027\u65f6\u95f4\u5e8f\u5217\u6570\u636e\uff08\u5982\u5b8f\u89c2\u7ecf\u6d4e\u5468\u671f\u3001\u80a1\u4ef7\u6ce2\u52a8\uff09\uff0c\u5c1d\u8bd5\u5e94\u7528\u5206\u5c94\u5206\u6790\u4e0e\u6df7\u6c8c\u8bc6\u522b\u65b9\u6cd5\u3002<\/li>\n
      • \u9605\u8bfb\u300aChaos and Order in the Capital Markets\u300b\u53ca\u76f8\u5173\u6587\u732e\uff0c\u8003\u5bdf\u6df7\u6c8c\u6846\u67b6\u5728\u91d1\u878d\u5e02\u573a\u5206\u6790\u4e2d\u7684\u5177\u4f53\u5e94\u7528\u4e0e\u5c40\u9650\u6027\u3002<\/li>\n<\/ul>\n

        \u7b2c\u4e09\u9636\u6bb5\uff085-6\u6708\uff09\uff1a\u7f16\u7a0b\u5b9e\u8df5<\/strong><\/p>\n

          \n
        • \u5229\u7528Python\u6216MATLAB\u5b9e\u73b0\u903b\u8f91\u65af\u8482\u6620\u5c04\uff08Logistic Map\uff09\u3001\u6d1b\u4f26\u8328\u65b9\u7a0b\u548c\u675c\u82ac\u632f\u5b50\uff08Duffing Oscillator\uff09\u7684\u6570\u503c\u6a21\u62df\uff0c\u4eb2\u81ea\u4f53\u9a8c\u5206\u5c94\u56fe\u7ed8\u5236\u3001\u500d\u5468\u671f\u5206\u5c94\u4e0e\u6df7\u6c8c\u5e26\u7684\u6d8c\u73b0\u8fc7\u7a0b\u3002<\/li>\n
        • \u6784\u5efa\u53ef\u89c6\u5316\u4ea4\u4e92\u5de5\u5177\uff0c\u4ee5\u53c2\u6570\u6ed1\u52a8\u7684\u65b9\u5f0f\u76f4\u89c2\u611f\u53d7\u5206\u5c94\u4e0e\u6df7\u6c8c\u7684\u8f6c\u53d8\u3002<\/li>\n<\/ul>\n

          \u7b2c\u56db\u9636\u6bb5\uff08\u957f\u671f\uff09\uff1a\u54f2\u5b66\u6574\u5408<\/strong><\/p>\n

            \n
          • \u7ed3\u5408\u590d\u6742\u6027\u79d1\u5b66\uff08Complexity\uff09\u3001\u590d\u6742\u9002\u5e94\u7cfb\u7edf\u7406\u8bba\uff08Complex Adaptive Systems\uff09\u8fdb\u884c\u5ef6\u4f38\u9605\u8bfb\uff0c\u601d\u8003\u6df7\u6c8c\u7406\u8bba\u5728\u8ba4\u8bc6\u8bba\u5c42\u9762\u4e0e\u73b0\u4ee3\u79d1\u5b66\u54f2\u5b66\u7684\u6df1\u5c42\u5bf9\u8bdd\u3002<\/li>\n
          • \u64b0\u5199\u4e00\u7bc7\u4e13\u9898\u8bba\u6587\uff0c\u8bba\u6790\u6df7\u6c8c\u7406\u8bba\u7684\u201c\u4e0d\u53ef\u9884\u6d4b\u6027\u201d\u547d\u9898\u5bf9\u793e\u4f1a\u79d1\u5b66\u65b9\u6cd5\u8bba\u7684\u65b9\u6cd5\u8bba\u542f\u793a\u3002<\/li>\n<\/ul>\n
            \n

            \u672c\u4e66\u8ba9\u6211\u4eec\u7406\u89e3\uff1a\u4e16\u754c\u5e76\u975e\u56e0\u4e3a\u6df7\u4e71\u800c\u96be\u4ee5\u6349\u6478\uff0c\u800c\u662f\u56e0\u4e3a\u5b83\u592a\u6709\u5e8f\u3001\u6709\u5e8f\u5230\u8fde\u6700\u7b80\u5355\u7684\u786e\u5b9a\u6027\u89c4\u5219\uff0c\u5728\u8db3\u591f\u957f\u7684\u65f6\u95f4\u5c3a\u5ea6\u4e0a\uff0c\u4e5f\u80fd\u7efd\u653e\u51fa\u4ee4\u4eba\u60ca\u53f9\u7684\u590d\u6742\u82b1\u6735\u3002\u8fd9\u6216\u8bb8\u624d\u662f\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u6700\u6df1\u6c89\u7684\u6559\u76ca\u3002<\/em><\/p>","protected":false},"excerpt":{"rendered":"

            \u300a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u6df7\u6c8c\uff08Steven Strogatz\uff09\u300b\u9605\u8bfb\u7b14\u8bb0 \u81ea\u52a8\u751f\u6210 | 2026-06-09 00:1 […]<\/p>","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2657","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/posts\/2657","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/deepbule.store\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2657"}],"version-history":[{"count":1,"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/posts\/2657\/revisions"}],"predecessor-version":[{"id":2658,"href":"https:\/\/deepbule.store\/index.php?rest_route=\/wp\/v2\/posts\/2657\/revisions\/2658"}],"wp:attachment":[{"href":"https:\/\/deepbule.store\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2657"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/deepbule.store\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2657"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/deepbule.store\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}