{"id":47662,"date":"2024-01-13T16:43:32","date_gmt":"2024-01-13T08:43:32","guid":{"rendered":"https:\/\/swarma.org\/?p=47662"},"modified":"2024-01-13T16:43:32","modified_gmt":"2024-01-13T08:43:32","slug":"%e6%8e%a2%e7%b4%a2%e5%a4%a7%e8%84%91%e4%b8%b4%e7%95%8c%e6%80%a7%e7%9a%84%e7%90%86%e8%ae%ba%e5%9f%ba%e7%a1%80%ef%bc%9a%e9%87%8d%e6%96%b0%e7%90%86%e8%a7%a3%e7%a5%9e%e7%bb%8f%e5%8a%a8%e5%8a%9b%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=47662","title":{"rendered":"\u63a2\u7d22\u5927\u8111\u4e34\u754c\u6027\u7684\u7406\u8bba\u57fa\u7840\uff1a\u91cd\u65b0\u7406\u89e3\u795e\u7ecf\u52a8\u529b\u5b66"},"content":{"rendered":"
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1. \u4e3a\u4ec0\u4e48\u7814\u7a76\u5927\u8111\u4e34\u754c\u6027\u7684\u7406\u8bba\u57fa\u7840<\/strong><\/span><\/p>\n

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1. \u89e3\u91ca\u4e3a\u4ec0\u4e48\u4e34\u754c\u6027\u5bf9\u5927\u8111\u5f88\u91cd\u8981<\/span><\/p>\n

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\u4e34\u754c\u6240\u9700\u7684\u6240\u6709\u7edf\u8ba1\u7269\u7406\u5173\u7cfb\u90fd\u88ab\u7cfb\u7edf\u9075\u5b88\uff0c\u4f46\u7279\u5f81\u53d8\u91cf\u7684\u5b9e\u9645\u503c\u4e0e\u5b8c\u7f8e\u4e34\u754c\u6027\u5b58\u5728\u8f7b\u5fae\u4e14\u4e0d\u7a33\u5b9a\u7684\u504f\u5dee\u3002\u8fd9\u4e9b\u504f\u5dee\u5b58\u5728\u4e14\u901a\u5e38\u4e0e\u6570\u636e\u566a\u58f0\u65e0\u5173\u3002<\/span><\/section>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\u88681 \u63cf\u8ff0\u5927\u8111\u4e34\u754c\u6027\u7684\u5173\u952e\u6982\u5ff5<\/span><\/section>\n

<\/section>\n
\u975e\u5e73\u8861\u6001 <\/strong>\u9996\u5148\uff0c\u4e0e\u5176\u4ed6\u751f\u7269\u7cfb\u7edf\u7c7b\u4f3c\uff0c\u5927\u8111\u901a\u5e38\u8868\u73b0\u51fa\u8fdc\u79bb\u5e73\u8861\u72b6\u6001\u7684\u65f6\u95f4\u6f14\u5316[10,11]\u3002\u8fd9\u4e9b\u504f\u79bb\u5e73\u8861\u7684\u73b0\u8c61\u662f\u7531\u4e8e\u591a\u79cd\u5185\u751f\u539f\u56e0\u800c\u4ea7\u751f\u7684[10,12]\uff0c\u6253\u7834\u4e86\u652f\u6301\u610f\u8bc6\u3001\u611f\u77e5\u548c\u9002\u5e94\u7684\u7ec6\u81f4\u5e73\u8861[11,12]\u3002\u56e0\u6b64\uff0c\u81f3\u5c11\u5728\u5927\u591a\u6570\u795e\u7ecf\u52a8\u529b\u5b66\u6a21\u578b\u548c\u7ecf\u9a8c\u6570\u636e\u96c6\u4e2d\uff0c\u795e\u7ecf\u52a8\u529b\u5b66\u6f5c\u5728\u7684\u4e34\u754c\u73b0\u8c61\u57fa\u672c\u4e0a\u662f\u975e\u5e73\u8861\u7684\uff0c\u4e0d\u80fd\u7528\u5e73\u8861\u7edf\u8ba1\u529b\u5b66\u6765\u8868\u5f81\u3002\u5728\u56fe1A\u4e2d\uff0c\u6211\u4eec\u8bf4\u660e\u4e86\u5e73\u8861\u52a8\u529b\u5b66\u548c\u975e\u5e73\u8861\u52a8\u529b\u5b66\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/span><\/section>\n

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\u5fae\u8c03\u4e0e\u81ea\u7ec4\u7ec7 <\/strong>\u5176\u6b21\uff0c\u5927\u8111\u4e34\u754c\u6027\u5b58\u5728\u4e24\u79cd\u673a\u5236\u89e3\u91ca\u3002\u4e00\u79cd\u673a\u5236\u662f\u6e90\u4e8e\u5916\u90e8\u5bf9\u5927\u8111\u7684\u64cd\u63a7[13,14]\uff0c\u6216\u81ea\u4e0a\u800c\u4e0b\u7684\u751f\u7269\u5b66\u8fc7\u7a0b\u4ece\u5927\u8111\u5168\u5c40\u5f71\u54cd\u795e\u7ecf\u52a8\u529b\u5b66[1]\u3002\u901a\u8fc7\u8fd9\u4e9b\u5916\u751f\u673a\u5236\uff0c\u795e\u7ecf\u52a8\u529b\u5b66\u88ab\u52a8\u5730\u5fae\u8c03<\/span>\uff08fine-tuning\uff09<\/span>\u6765\u9760\u8fd1\u6216\u8fdc\u79bb\u666e\u901a\u4e34\u754c\u6027<\/span>\uff08OC, ordinary criticality\uff09<\/span>\u3002\u53e6\u4e00\u79cd\u673a\u5236\u5305\u62ec\u6240\u6709\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u5185\u6e90\u6027\u56e0\u7d20[15]\u3002\u8fd9\u4e9b\u673a\u5236\u5728\u795e\u7ecf\u52a8\u529b\u5b66\u4e0a\u5c40\u90e8\u4f5c\u7528\uff0c\u5f62\u6210\u53cd\u9988\u63a7\u5236\u73af\u6765\u652f\u6301\u795e\u7ecf\u52a8\u529b\u5b66\u5411\u4e34\u754c\u70b9\u7684\u81ea\u7ec4\u7ec7\u884c\u4e3a\u3002\u8fd9\u79cd\u81ea\u53d1\u51fa\u73b0\u7684\u5927\u8111\u4e34\u754c\u6027\u88ab\u63a8\u6d4b\u4e3a\u4e00\u79cd\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027<\/span>\uff08SOC, self-organized criticality\uff09<\/span>[16]\u3002\u5728\u56fe1B\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u5927\u8111\u4e2d\u666e\u901a\u4e34\u754c\u6027\u548c\u51c6\u4e34\u754c\u6027\u7684\u6982\u5ff5\u56fe\u793a\u3002<\/span><\/section>\n

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\u56fe1 \u5927\u8111\u4e34\u754c\u6027\u7684\u6982\u5ff5\u56fe\u3002\uff08A\uff09\u5e73\u8861\u548c\u975e\u5e73\u8861\u52a8\u529b\u5b66\u4e4b\u95f4\u7684\u5dee\u5f02\u3002\u5927\u8111\u72b6\u6001\u7531\u4e09\u4e2a\u7cfb\u7edf\u7ec4\u6210\u90e8\u5206\u6765\u8868\u5f81\u3002\u6211\u4eec\u4e3e\u4f8b\u8bf4\u660e\u4e86\u8fd9\u4e9b\u72b6\u6001\u4e4b\u95f4\u7684\u975e\u5e73\u8861\u52a8\u529b\u5b66\u5b9e\u4f8b\u3002\uff08B\uff09\u5916\u6e90\u673a\u5236\u7684\u5fae\u8c03\u4f7f\u5927\u8111\u4ece\u975e\u4e34\u754c\u72b6\u6001\uff08\u5de6\u4e0a\uff09\u8fdb\u5316\u5230\u4e34\u754c\u72b6\u6001\uff08\u53f3\u4e0a\uff09\u3002\u5185\u6e90\u6027\u673a\u5236\u4f7f\u5927\u8111\u80fd\u591f\u81ea\u7ec4\u7ec7\u4ece\u975e\u4e34\u754c\u72b6\u6001\uff08\u5de6\u4e0b\uff09\u5230\u4e34\u754c\u72b6\u6001\uff08\u53f3\u4e0b\uff09\u3002\uff08C\uff09\u589e\u52a0\u523a\u6fc0\u5f3a\u5ea6\u4f1a\u6269\u5927\u51c6\u4e34\u754c\u7cfb\u7edf\u4e2d\u5b8c\u7f8e\u4e34\u754c\u70b9\u5468\u56f4\u7684\u51c6\u4e34\u754c\u533a\u57df\u3002\uff08D\uff09\u81ea\u7ec4\u7ec7\u51c6\u4e34\u754c\u7cfb\u7edf\u903c\u8fd1\u4e34\u754c\u70b9\u7684\u8fc7\u7a0b\u7531\u4e24\u4e2a\u9636\u6bb5\u7ec4\u6210\u3002\u5728\u7b2c\u4e00\u9636\u6bb5\uff0c\u5927\u8111\u57fa\u4e8e\u67d0\u4e9b\u5185\u6e90\u673a\u5236\u4ece\u975e\u4e34\u754c\u72b6\u6001\u81ea\u7ec4\u7ec7\u5230\u51c6\u4e34\u754c\u533a\u57df\u3002\u5728\u7b2c\u4e8c\u9636\u6bb5\uff0c\u9700\u8981\u989d\u5916\u7684\u5916\u6e90\u673a\u5236\u5c06\u5927\u8111\u5fae\u8c03\u5230\u4e34\u754c\u70b9\u3002\u5426\u5219\uff0c\u5927\u8111\u53ea\u4f1a\u5728\u51c6\u4e34\u754c\u533a\u5185\u5f98\u5f8a\u3002\uff08E\uff09\u4ece\u654f\u611f\u6027\u89d2\u5ea6\u770b\u56db\u79cd\u5927\u8111\u4e34\u754c\u6027\u7684\u5dee\u5f02\u3002\u5bf9\u4e8e\u6807\u51c6\u7684\u5927\u8111\u4e34\u754c\u6027\uff08\u4f8b\u5982\uff0c\u666e\u901a\u4e34\u754c\u6027\u548c\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027\uff09\uff0c\u654f\u611f\u6027\u5728\u4e34\u754c\u70b9\u53d8\u5f97\u53d1\u6563\uff08\u5373\u65e0\u9650\uff09\u3002\u5bf9\u4e8e\u975e\u6807\u51c6\u7684\u5927\u8111\u4e34\u754c\u6027\uff08\u4f8b\u5982\uff0c\u51c6\u4e34\u754c\u6027\u548c\u81ea\u7ec4\u7ec7\u51c6\u4e34\u754c\u6027\uff09\uff0c\u654f\u611f\u6027\u59cb\u7ec8\u662f\u975e\u53d1\u6563\u7684\uff08\u5373\u6709\u9650\u7684\uff09\u3002\u51c6\u4e34\u754c\u533a\u5b9a\u4e49\u4e3a\u654f\u611f\u6027\u503c\u4e0d\u5c0f\u4e8e\u7279\u5b9a\u9608\u503c\uff08\u4f8b\u5982\u534a\u6700\u5927\u503c\uff09\u7684\u6240\u6709\u63a7\u5236\u53c2\u6570\u7684\u96c6\u5408\u3002\uff08F\uff09\u56db\u79cd\u5927\u8111\u4e34\u754c\u6027\u7684\u5171\u6027\u548c\u5dee\u5f02\u3002<\/span><\/p>\n


<\/section>\n
\u6807\u51c6\u4e34\u754c\u4e0e\u51c6\u4e34\u754c<\/strong> \u7b2c\u4e09\uff0c\u7531\u4e8e\u523a\u6fc0\u9a71\u52a8\u6216\u5185\u6e90\u6027\u56e0\u7d20\uff0c\u5927\u8111\u4e34\u754c\u72b6\u6001\u7ecf\u5e38\u4ee5\u975e\u6807\u51c6\u5f62\u5f0f\u53d1\u751f\u3002\u5728\u7279\u5f81\u53d8\u91cf\u7684\u5b9e\u9645\u503c\u4e0a\u53ef\u4ee5\u770b\u5230\u4e0e\u5b8c\u7f8e\u5927\u8111\u4e34\u754c\u6027\u7684\u8f7b\u5fae\u4e14\u4e0d\u7a33\u5b9a\u7684\u504f\u5dee\uff0c\u540c\u65f6\u8fd9\u4e9b\u5b9e\u9645\u7279\u5f81\u53d8\u91cf\u4f9d\u7136\u5728\u6807\u51c6\u4e34\u754c\u6027\u6240\u9700\u7684\u7edf\u8ba1\u7269\u7406\u5173\u7cfb\u9644\u8fd1\uff0c\u56e0\u6b64\u51c6\u4e34\u754c\u6027\u4e0e\u975e\u4e34\u754c\u6027\u533a\u5206\u5f00\u6765[7]\u3002<\/span><\/section>\n

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\u5bf9\u4e8e\u666e\u901a\u4e34\u754c\u6027<\/span>\uff08OC\uff09<\/span>\uff0c\u5176\u975e\u6807\u51c6\u5f62\u5f0f\u88ab\u79f0\u4e3a\u51c6\u4e34\u754c\u6027<\/strong><\/span>\uff08qC\uff0cQuasi-criticality\uff09<\/span>[7,17]\u3002\u591a\u79cd\u673a\u5236\u53ef\u4ee5\u8feb\u4f7f\u5927\u8111\u504f\u79bbOC\u5e76\u8868\u73b0\u51faqC\u795e\u7ecf\u52a8\u529b\u5b66\uff0c\u5176\u4e2d\u523a\u6fc0\u5bfc\u81f4\u7684\u51c6\u4e34\u754c\u53ef\u80fd\u662f\u6700\u5e38\u89c1\u7684\u4e00\u79cd\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u8db3\u591f\u5f3a\u7684\u523a\u6fc0\u9a71\u52a8\u53ef\u4ee5\u6355\u83b7\u751a\u81f3\u63a7\u5236\u795e\u7ecf\u52a8\u529b\u5b66\u3002\u4e0e\u5916\u90e8\u8f93\u5165\u6291\u5236\u4e0d\u89c4\u5219\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u60c5\u51b5\u7c7b\u4f3c\uff0c\u592a\u5f3a\u7684\u523a\u6fc0\u53ef\u80fd\u4f1a\u5f15\u8d77\u5f3a\u70c8\u4f46\u4e0d\u6613\u53d8\u5316\u7684\u795e\u7ecf\u52a8\u529b\u5b66\uff0c\u4f7f\u5927\u8111\u504f\u79bb\u5b8c\u7f8e\u7684\u4e34\u754c\u70b9\u3002\u7531\u523a\u6fc0\u5f3a\u5ea6\u03bd\u3001\u4e0d\u5e94\u671f\u957f\u5ea6\u03c4\u3001\u5206\u652f\u6bd4\u03ba\u63cf\u8ff0\u5927\u8111\u5728Widom\u7ebf\u9644\u8fd1\u7684qC\u5c31\u662f\u4e00\u4e2a\u5f88\u597d\u7684\u4f8b\u5b50\uff0c\u5728Widom\u7ebf\u4e0a\u795e\u7ecf\u5143\u52a8\u529b\u5b66\u7684\u654f\u611f\u6027\u6700\u5927\u5316\uff0c\u9760\u8fd1Widom\u7ebf\u8868\u660e\u5927\u8111\u4e2d\u5b58\u5728qC\uff0c\u540c\u65f6\u4e0eWidom\u7ebf\u7684\u663e\u7740\u504f\u5dee\u8868\u660e\u975e\u4e34\u754c\u6027[7,17]\u3002\u5728\u56fe1C\u4e2d\uff0c\u6211\u4eec\u4ece\u6982\u5ff5\u4e0a\u8bf4\u660e\u4e86\u523a\u6fc0\u5982\u4f55\u5728\u5927\u8111\u4e2d\u6697\u793aqC\u3002\u5728\u56fe2D\u4e2d\uff0c\u8be6\u7ec6\u5c55\u793a\u4e86Widom\u7ebf\u4e0a\u7684qC\u3002<\/span><\/section>\n

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\u5173\u4e8eSOC\uff0c\u5b83\u7684\u975e\u6807\u51c6\u5f62\u5f0f\u662f\u6839\u636e\u7edf\u8ba1\u7269\u7406\u5b66\u6807\u51c6\u5b9a\u4e49\u7684\u3002\u5b8c\u7f8e\u7684SOC\u53ea\u5b58\u5728\u4e8e\u4fdd\u5b88\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u4e2d\uff0c\u5176\u4e2d\u7cfb\u7edf\u80fd\u91cf<\/span>\uff08\u5373\u795e\u7ecf\u6d3b\u52a8\uff09<\/span>\u8981\u4e48\u5728\u7cfb\u7edf\u5185\u4fdd\u6301\u4e0d\u53d8\uff0c\u53ea\u5728\u7cfb\u7edf\u8fb9\u754c\u4e0a\u6d88\u6563\uff0c\u8981\u4e48\u5728\u7cfb\u7edf\u5185\u90e8\u6d88\u6563<\/span>\uff08\u5373\u4f53\u79ef\u8017\u6563\uff09<\/span>\uff0c\u5176\u8017\u6563\u7387\u5728\u7cfb\u7edf\u5c3a\u5bf8\u6781\u9650\u4e0b\u9010\u6e10\u6d88\u5931[18]\u3002\u5728\u795e\u7ecf\u52a8\u529b\u5b66\u4e0d\u662f\u4fdd\u5b88\u7684\u66f4\u4e00\u822c\u60c5\u51b5\u4e0b\uff0c\u4efb\u4f55\u4f53\u79ef\u8017\u6563\u7387\u90fd\u53ef\u4ee5\u7834\u574f\u5b8c\u7f8e\u7684SOC[19]\u3002\u66f4\u5f3a\u7684\u4f53\u79ef\u8017\u6563\u610f\u5473\u7740\u66f4\u5927\u7684\u504f\u79bb\u5b8c\u7f8e\u7684SOC\u3002\u56e0\u6b64\uff0c\u4e0e\u6807\u51c6SOC\u4e0d\u540c\uff0c\u975e\u4fdd\u5b88\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u81ea\u7ec4\u7ec7\u8fc7\u7a0b\u53ea\u80fd\u4f7f\u5927\u8111\u5f98\u5f8a\u5728\u4e34\u754c\u70b9\u9644\u8fd1\u3002\u4efb\u4f55\u8fdb\u4e00\u6b65\u63a5\u8fd1\u4e34\u754c\u70b9\u90fd\u9700\u8981\u901a\u8fc7\u989d\u5916\u7684\u5916\u6e90\u673a\u5236\u5bf9\u79e9\u5e8f\u53c2\u6570\u8fdb\u884c\u7cbe\u7ec6\u8c03\u6574\u3002\u8fd9\u4e2a\u975e\u4fdd\u5b88\u7684\u81ea\u7ec4\u7ec7\u8fc7\u7a0b\u88ab\u79f0\u4e3a\u81ea\u7ec4\u7ec7\u51c6\u4e34\u754c\u6027<\/strong><\/span>\uff08SOqC\uff0cSelf-organized quasi-criticality\uff09<\/span>[20]\u3002\u4e0e\u4fdd\u5b88\u52a8\u529b\u5b66\u4e2d\u7684SOC\u7c7b\u4f3c\uff0c\u795e\u7ecf\u53ef\u5851\u6027[21]\u3001Hebbian\u89c4\u5219[22]\u3001\u77ed\u671f\u7a81\u89e6\u6291\u5236\u548c\u4e0e\u5c16\u5cf0\u76f8\u5173\u9608\u503c\u589e\u52a0[23]\u6216\u4e0e\u7f51\u7edc\u62d3\u6251\u76f8\u5173\u7684\u6291\u5236\u6027\u53ef\u5851\u6027[24]\u53ef\u4ee5\u4f5c\u4e3aSOqC\u7684\u6f5c\u5728\u81ea\u7ec4\u7ec7\u673a\u5236\u3002\u7531\u4e8e\u5728\u5b9e\u8bc1\u6570\u636e\u4e2d\u7eaf\u7cb9\u7684\u4fdd\u5b88\u578b\u795e\u7ecf\u52a8\u529b\u5b66\u76f8\u5bf9\u8f83\u5c11[15,19]\uff0c\u6211\u4eec\u8ba4\u4e3aSOqC\u5728\u5927\u8111\u4e2d\u6bd4SOC\u66f4\u4e3a\u5e38\u89c1\u3002\u5728\u56fe1D\u4e2d\uff0c\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6982\u5ff5\u6027\u7684\u4f8b\u5b50\uff0c\u63cf\u8ff0\u4e86\u5927\u8111\u5728SOqC\u7684\u4f5c\u7528\u4e0b\u5411\u4e34\u754c\u70b9\u63a5\u8fd1\u7684\u4e24\u4e2a\u9636\u6bb5\u3002<\/span><\/section>\n

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\u5927\u8111\u4e34\u754c\u6027\u7684\u5206\u7c7b <\/strong>\u4e0a\u8ff0\u8ba8\u8bba\u5df2\u7ecf\u7ed9\u51fa\u4e86\u5927\u8111\u4e34\u754c\u6027\u7684\u5206\u7c7b\u6846\u67b6\uff0c\u5373\u666e\u901a\u4e34\u754c\u6027<\/span>\uff08OC\uff09<\/span>\u3001\u51c6\u4e34\u754c\u6027<\/span>\uff08qC\uff09<\/span>\u3001\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027<\/span>\uff08SOC\uff09<\/span>\u548c\u81ea\u7ec4\u7ec7\u51c6\u4e34\u754c\u6027<\/span>\uff08SOqC\uff09<\/span>\u3002\u5728\u56fe1E\u4e2d\uff0c\u6211\u4eec\u4ece\u654f\u611f\u6027\u7684\u89d2\u5ea6\u6bd4\u8f83\u4e86\u8fd9\u56db\u79cd\u7c7b\u578b\u7684\u5927\u8111\u4e34\u754c\u6027\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5728\u6807\u51c6\u4e34\u754c\u6027\u7684\u5927\u8111<\/span>\uff08\u4f8b\u5982OC\u548cSOC\uff09<\/span>\u4e2d\uff0c\u654f\u611f\u6027\u5728\u4e34\u754c\u70b9\u53d1\u6563\uff0c\u800c\u5728\u975e\u6807\u51c6\u4e34\u754c\u6027\u7684\u5927\u8111<\/span>\uff08\u4f8b\u5982 qC \u548c SOqC\uff09<\/span>\u7684\u51c6\u4e34\u754c\u6027\u533a\u57df\u4e2d\uff0c\u654f\u611f\u6027\u4e0d\u4f1a\u53d1\u6563\u3002\u5728\u56fe1F\u4e2d\uff0c\u6211\u4eec\u603b\u7ed3\u4e86\u6211\u4eec\u8bc4\u8ff0\u4e2d\u8ba8\u8bba\u7684\u8fd9\u56db\u79cd\u5927\u8111\u4e34\u754c\u6027\u4e4b\u95f4\u7684\u5171\u6027\u548c\u5dee\u5f02\u3002<\/span><\/section>\n

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3. \u795e\u7ecf\u5143\u96ea\u5d29\u548c\u5927\u8111\u4e34\u754c\u6027<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u4e3a\u4e86\u8bc6\u522b\u5927\u8111\u4e2d\u6f5c\u5728\u7684\u4e34\u754c\u70b9\uff0c\u7814\u7a76\u4eba\u5458\u5b9e\u9645\u4e0a\u5c06\u795e\u7ecf\u52a8\u529b\u5b66\u63cf\u8ff0\u4e3a\u5177\u6709\u5438\u6536\u72b6\u6001\u548c\u96ea\u5d29\u884c\u4e3a\u7684\u7269\u7406\u7cfb\u7edf\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u9700\u8981\u8003\u8651\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u4f20\u64ad\uff0c\u5176\u4e2d\u795e\u7ecf\u5143\u8981\u4e48\u88ab\u6fc0\u6d3b<\/span>\uff08\u201c\u5f00\u542f\u201d\u72b6\u6001\uff09<\/span>\uff0c\u8981\u4e48\u4fdd\u6301\u6c89\u9ed8<\/span>\uff08\u201c\u5173\u95ed\u201d\u72b6\u6001\uff09<\/span>\u3002\u6c89\u9ed8\u795e\u7ecf\u5143\u53ef\u4ee5\u6309\u7167\u7531\u6fc0\u6d3b\u7684\u7a81\u89e6\u524d\u795e\u7ecf\u5143\u7684\u6570\u91cf\u548c\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8026\u5408\u5f3a\u5ea6\u03b8\u5b9a\u4e49\u7684\u6982\u7387\u88ab\u6fc0\u6d3b\u3002\u6fc0\u6d3b\u7684\u795e\u7ecf\u5143\u4f1a\u4ee5\u6052\u5b9a\u7684\u901f\u7387\u81ea\u53d1\u5730\u53d8\u5f97\u6c89\u9ed8\u3002\u8fd9\u4e9b\u5b9a\u4e49\u81ea\u7136\u652f\u6301\u533a\u5206\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u4e0d\u540c\u76f8\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u56de\u987e\u4e86\u795e\u7ecf\u79d1\u5b66\u4e2d\u5e38\u89c1\u7684\u4e24\u79cd\u76f8\u53d8\u8fc7\u7a0b\u3002<\/span><\/section>\n

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\u5438\u6536\u76f8\u548c\u6d3b\u8dc3\u76f8<\/strong><\/span>\uff08absorbing vs. active\uff09<\/span>\u3002\u5438\u6536\u76f8\u662f\u6307\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8026\u5408\u8f83\u5f31\u5e76\u4e14\u6240\u6709\u795e\u7ecf\u5143\u6700\u7ec8\u53d8\u5f97\u6c89\u9ed8\u7684\u60c5\u51b5[25]\u3002\u4e00\u65e6\u795e\u7ecf\u52a8\u529b\u5b66\u8fc7\u7a0b\u6d88\u5931\uff0c\u5b83\u5c31\u65e0\u6cd5\u81ea\u884c\u91cd\u65b0\u51fa\u73b0\u3002\u5927\u8111\u9700\u8981\u65b0\u7684\u9a71\u52a8\u6765\u89e6\u53d1\u65b0\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u6d3b\u8dc3\u76f8\u5bf9\u5e94\u4e8e\u201c\u5f00\u542f\u201d\u72b6\u6001\u5728\u5177\u6709\u5f3a\u8026\u5408\u7684\u795e\u7ecf\u5143\u4e4b\u95f4\u4f20\u64ad\u7684\u60c5\u51b5\uff0c\u4ece\u800c\u5bfc\u81f4\u7a33\u5b9a\u7684\u81ea\u6211\u7ef4\u6301\u795e\u7ecf\u52a8\u529b\u5b66<\/span>\uff08\u4f8b\u5982\uff0c\u5927\u8111\u4e2d\u6d3b\u8dc3\u795e\u7ecf\u5143\u7684\u975e\u96f6\u65f6\u95f4\u548c\u6574\u4f53\u5e73\u5747\u5bc6\u5ea6\uff09<\/span>\u3002\u5728\u56fe2A\u4e2d\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u795e\u7ecf\u96ea\u5d29\u3001\u81ea\u6211\u7ef4\u6301\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u548c\u6d88\u5931\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u6982\u5ff5\u5b9e\u4f8b\u3002\u5c06\u03c1(t)\u8868\u793a\u4e3at\u65f6\u523b\u6d3b\u8dc3\u795e\u7ecf\u5143\u7684\u5bc6\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5730\u5c060\u65f6\u523b\u6d3b\u8dc3\u795e\u7ecf\u5143\u89e6\u53d1\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u8fc7\u7a0b\u7684\u5438\u6536\u548c\u6d3b\u8dc3\u76f8\u8868\u793a\u4e3a<\/span><\/section>\n

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\u540c\u6b65\u76f8\u548c\u5f02\u6b65\u76f8<\/strong><\/span>\uff08synchronous vs. asynchronous\uff09<\/span>\u3002\u987e\u540d\u601d\u4e49\uff0c\u8fd9\u4e24\u4e2a\u76f8\u5206\u522b\u5bf9\u5e94\u4e8e\u795e\u7ecf\u6d3b\u52a8\u4e2d\u540c\u6b65\u51fa\u73b0\u6216\u6d88\u5931\u7684\u60c5\u51b5[26]\u3002\u540c\u6b65\u662f\u6307\u201c\u5f00\u542f\u201d\u72b6\u6001\u4ee5\u632f\u8361<\/span>\uff08\u5c3d\u7ba1\u4e0d\u662f\u4e25\u683c\u5468\u671f\u6027\uff09<\/span>\u65b9\u5f0f\u51fa\u73b0\u7684\u60c5\u51b5\u3002\u4e3a\u4e86\u91cf\u5316\u5176\u6f5c\u5728\u5b58\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u53d8\u5f02\u7cfb\u6570<\/span>\uff08CV\uff09<\/span>[26]\u6216Kuramoto\u5e8f\u53c2\u91cf[27]\u6765\u6d4b\u91cf\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u53d8\u5f02\u6027\u3002CV\u53ef\u4ee5\u4ece\u4e0d\u540c\u7684\u89d2\u5ea6\u5b9a\u4e49\uff0c\u4f46\u6700\u5e38\u89c1\u7684\u5b9a\u4e49\u662f\u6807\u51c6\u5dee\u4e0e\u5cf0\u95f4\u95f4\u9694\u957f\u5ea6\u5e73\u5747\u503c\u4e4b\u95f4\u7684\u6bd4\u7387\u3002CV\u503c\u8d8a\u9ad8\u610f\u5473\u7740\u540c\u6b65\u6027\u8d8a\u5dee\u3002\u5bf9\u4e8e\u5927\u591a\u6570\u795e\u7ecf\u52a8\u529b\u5b66\u6570\u636e\uff0c\u533a\u5206\u540c\u6b65\u548c\u5f02\u6b65\u76f8\u7684CV\u9608\u503c\u7684\u7ecf\u9a8c\u9009\u62e9\u53ef\u80fd\u662f<\/sub>1\u6216<\/sub>3\/2[1]\u3002Kuramoto\u5e8f\u53c2\u91cf\u03c9\u2208[0, 1]<\/span>\u57fa\u4e8eKuramoto\u632f\u8361\u5668\u6a21\u578b\u6d4b\u91cf\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u76f8\u5e72\u7a0b\u5ea6\u3002\u5f53\u03c9=1\u65f6\uff0c\u5b8c\u7f8e\u540c\u6b65\u51fa\u73b0\uff1b\u5f53\u03c9=0<\/span>\u65f6\uff0c\u5b8c\u7f8e\u540c\u6b65\u6d88\u5931[27]\u3002<\/span><\/section>\n

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\u4e0a\u8ff0\u4e24\u7ec4\u76f8\u7684\u8fb9\u754c\u5c31\u662f\u4e34\u754c\u70b9\uff0c\u6b64\u65f6\u5927\u8111\u5904\u4e8e\u8868\u73b0\u51fa\u81ea\u6211\u7ef4\u6301<\/span>\uff08\u5bf9\u4e8e\u5438\u6536\u548c\u6d3b\u8dc3\u76f8\uff09<\/span>\u6216\u540c\u6b65<\/span>\uff08\u5bf9\u4e8e\u540c\u6b65\u548c\u5f02\u6b65\u76f8\uff09<\/span>\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u8fb9\u7f18\u3002\u5bf9\u5438\u6536\u6216\u5f02\u6b65\u76f8\u7684\u6270\u52a8<\/span>\uff08\u4f8b\u5982\uff0c\u795e\u7ecf\u5143\u4e4b\u95f4\u201c\u5f00\u542f\u201d\u72b6\u6001\u7684\u4f20\u64ad\uff09<\/span>\u6ca1\u6709\u7279\u5f81\u5bff\u547d\u548c\u5927\u5c0f\u3002\u8fd9\u4e9b\u6270\u52a8<\/span>\uff08\u79f0\u4e3a\u795e\u7ecf\u96ea\u5d29\uff09<\/span>\u9884\u8ba1\u5728\u5176\u751f\u547d\u5468\u671f\u4e2d\u8868\u73b0\u51fa\u5e42\u5f8b\u7279\u6027<\/span>\uff08\u5b8c\u5168\u6c89\u9ed8\u65f6\u671f\u4e4b\u95f4\u795e\u7ecf\u5143\u7b2c\u4e00\u6b21\u548c\u6700\u540e\u4e00\u6b21\u6fc0\u6d3b\u4e4b\u95f4\u7684\u65f6\u95f4\u5dee\uff09<\/span>\u548c\u5927\u5c0f<\/span>\uff08\u6d3b\u52a8\u795e\u7ecf\u5143\u7684\u6570\u91cf\u4ee5\u53ca\u504f\u79fb\uff09<\/span>\u5206\u5e03\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u795e\u7ecf\u96ea\u5d29\u7684\u51fa\u73b0\u610f\u5473\u7740\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u51cf\u6162\uff0c\u5373\u6ce2\u52a8\u4ece\u5feb<\/span>\uff08\u6307\u6570\uff09<\/span>\u5230\u6162<\/span>\uff08\u5e42\u5f8b\uff09<\/span>\u53d8\u5316\u540e\u5927\u8111\u72b6\u6001\u5411\u57fa\u7ebf\u72b6\u6001\u6062\u590d\u7684\u8fc7\u7a0b\u3002\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u52a8\u6001\u7a33\u5b9a\u6027\u53d7\u5230\u7f13\u6162\u6062\u590d\u7684\u9650\u5236\uff0c\u56e0\u6b64\u4e0d\u80fd\u7a33\u5065\u5730\u62b5\u6d88\u6270\u52a8\u3002\u56e0\u6b64\uff0c\u5728\u5fae\u89c2\u5c3a\u5ea6\u4e0a\u5f15\u53d1\u7684\u5c0f\u6270\u52a8\u4ecd\u7136\u53ef\u80fd\u4f7f\u5927\u8111\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4e0a\u53d1\u751f\u6025\u5267\u53d8\u5316<\/strong>[28]\u3002\u5728\u56fe2B\u4e2d\uff0c\u6211\u4eec\u6982\u5ff5\u6027\u5730\u8bf4\u660e\u4e86\u5f53\u5927\u8111\u63a5\u8fd1\u4e34\u754c\u70b9\u6216\u51c6\u4e34\u754c\u533a\u57df\u65f6\u6062\u590d\u8fc7\u7a0b\u5982\u4f55\u51cf\u6162\u3002<\/span><\/section>\n

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\u795e\u7ecf\u96ea\u5d29\u548c\u5927\u8111\u4e34\u754c\u6027\u4e4b\u95f4\u7684\u5173\u7cfb\u7ecf\u5e38\u88ab\u5ffd\u89c6\u6216\u8bef\u89e3\u3002\u5355\u72ec\u7684\u795e\u7ecf\u96ea\u5d29\u6570\u636e\u4e0d\u8db3\u4ee5\u786e\u5b9a\u5927\u8111\u4e34\u754c\u6027\u7684\u5177\u4f53\u7c7b\u578b<\/span>\uff08\u5373 OC\u3001qC\u3001SOC \u548c SOqC\uff09<\/span>\uff0c\u9664\u975e\u63d0\u4f9b\u6709\u5173\u795e\u7ecf\u96ea\u5d29\u51fa\u73b0\u673a\u5236\u7684\u9644\u52a0\u4fe1\u606f<\/span>\uff08\u4f8b\u5982\uff0c\u5982\u679c\u795e\u7ecf\u52a8\u529b\u5b66\u662f\u5b88\u6052\u7684\u6216\u81ea\u7ec4\u7ec7\uff09<\/span>\u3002\u4e3a\u4e86\u63a2\u7d22\u5177\u4f53\u7c7b\u578b\u7684\u5927\u8111\u4e34\u754c\u6027\uff0c\u7814\u7a76\u4eba\u5458\u9700\u8981\u6839\u636e\u4e0d\u540c\u7684\u63a7\u5236\u53c2\u6570\u660e\u786e\u5730\u7ed9\u51fa\u5176\u5b9a\u4e49\u548c\u5e8f\u53c2\u91cf\u3002\u6ca1\u6709\u4e25\u683c\u5b9a\u4e49\u63a7\u5236\u548c\u5e8f\u53c2\u91cf\u7684\u5927\u8111\u4e34\u754c\u5047\u8bbe\u662f\u6ca1\u6709\u4fe1\u606f\u7684[28]\u3002\u4e3a\u4e86\u5448\u73b0\u6982\u5ff5\u5b9e\u4f8b\uff0c\u6211\u4eec\u5728\u56fe2\u4e2d\u8bf4\u660e\u4e86\u56db\u79cd\u53ef\u80fd\u7684\u4e34\u754c\u73b0\u8c61\uff0c\u6bcf\u79cd\u73b0\u8c61\u5bf9\u5e94\u4e8e\u4e00\u79cd\u5177\u4f53\u7684\u5927\u8111\u4e34\u754c\u7c7b\u578b\u3002<\/span><\/section>\n

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4. \u5927\u8111\u4e34\u754c\u6027\u7684\u5e73\u5747\u573a\u548c\u968f\u673a\u573a\u8bba<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u795e\u7ecf\u79d1\u5b66\u5bb6\u5728\u7814\u7a76\u4e0d\u540c\u4e34\u754c\u6027\u65f6\u9762\u4e34\u7684\u4e3b\u8981\u6311\u6218\u4e4b\u4e00\u662f\u5982\u4f55\u7406\u89e3\u5b83\u4eec\u7684\u7406\u8bba\u5173\u7cfb[29]\u3002\u514b\u670d\u8fd9\u4e00\u6311\u6218\u5bf9\u4e8e\u7406\u89e3\u4e3a\u4ec0\u4e48\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u7406\u8bba\u5de5\u5177\u9a8c\u8bc1\u4e0d\u540c\u7c7b\u578b\u7684\u5927\u8111\u4e34\u754c\u6027\u7684\u5b58\u5728\u81f3\u5173\u91cd\u8981\u3002\u4e3a\u4e86\u8fdb\u884c\u7b80\u6d01\u548c\u5168\u9762\u7684\u56de\u987e\uff0c\u6211\u4eec\u9996\u5148\u5173\u6ce8\u5438\u6536\u76f8\u548c\u6d3b\u8dc3\u76f8\u4e4b\u95f4\u7684\u5927\u8111\u4e34\u754c\u6027\u3002\u6211\u4eec\u6982\u62ec\u4e86[20,30]\u4e2d\u7684\u60f3\u6cd5\u4ee5\u63d0\u51fa\u4e00\u4e2a\u53ef\u80fd\u7684\u6846\u67b6\u3002<\/span><\/section>\n

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OC\u7684Langevin\u65b9\u7a0b <\/strong>\u4e00\u822c\u6765\u8bf4\uff0c\u5438\u6536\u76f8\u548c\u6d3b\u8dc3\u76f8\u7a7a\u95f4\u4e2d\u7684\u5927\u8111\u4e34\u754c\u6027\u4e0e\u5b9a\u5411\u6e17\u900f\u6709\u5173[6]\uff0c\u8fd9\u662f\u4e00\u79cd\u8fde\u7eed\u76f8\u53d8\u5230\u5438\u6536\u6001\u7684\u666e\u9002\u7c7b<\/span>\uff08\u666e\u9002\u7c7b\u6307\u5177\u6709\u76f8\u540c\u6807\u5ea6\u5c5e\u6027\u7684\u6240\u6709\u7cfb\u7edf\u7684\u96c6\u5408\uff09<\/span>[31]\u3002\u5b9a\u5411\u6e17\u6d41\u7406\u8bba\u6700\u521d\u6db5\u76d6\u4e86OC\u73b0\u8c61\u3002\u6211\u4eec\u4ece\u7ecf\u5178Reggeon\u573a\u8bba\u7684\u53d8\u4f53\u5f00\u59cb\uff0c\u8fd9\u662f\u5438\u6536\u76f8\u53d8\u7684\u6700\u7b80\u5355\u63cf\u8ff0[32]\u3002\u6d3b\u52a8\u795e\u7ecf\u5143\u573a<\/span>\u7684Langevin\u65b9\u7a0b\u53ef\u4ee5\u88ab\u5b9a\u4e49\u4e3a\uff1a<\/span><\/section>\n

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\u5176\u4e2d<\/sub><\/span>\u8868\u793a\u7a7a\u95f4\u5750\u6807\uff0c <\/sub>\u662f\u6269\u6563\u56e0\u5b50\uff0c<\/sub><\/span>\u662f\u566a\u58f0\u56e0\u5b50\uff0c<\/sub><\/span>\u51fd\u6570\u662f\u65f6\u7a7a\u57df\u7684\u566a\u58f0\u9879\u3002\u4e00\u822c\u6765\u8bf4\uff0c<\/sub><\/span>\u53cd\u6620\u4e86\u795e\u7ecf\u5143\u6d3b\u52a8\u7684\u96c6\u4f53\u6270\u52a8\uff0c\u8fd9\u4e9b\u6270\u52a8\u5728\u5438\u6536\u76f8\u4f1a\u6d88\u5931\u4e3a\u96f6\u3002<\/span>\u9879\u53cd\u6620\u4e86\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u4f20\u64ad\uff0c<\/span>\u51fd\u6570\u5b9a\u4e49\u4e86\u6839\u636e<\/span>\u4f20\u64ad\u7684\u80fd\u91cf<\/span>\uff08\u5982\u819c\u7535\u4f4d\uff09<\/span>\uff0c\u8fd9\u4e2a\u51fd\u6570\u968f\u7740\u5916\u90e8\u9a71\u52a8<\/span>\u589e\u52a0\uff0c\u968f\u7740\u4f53\u8017\u6563<\/span>\u51cf\u5c0f\u3002\u8fd9\u91cc\u6211\u4eec\u8981\u6c42\u795e\u7ecf\u5143\u5bc6\u5ea6\u548c\u80fd\u91cf\u59cb\u7ec8\u975e\u8d1f<\/span>\u3002<\/span><\/section>\n

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\u5f88\u663e\u7136\uff0c<\/sub>\u4f7f\u5f97\u795e\u7ecf\u52a8\u529b\u5b66\u6700\u7ec8\u6d88\u5931<\/span>\uff08\u5bf9\u5e94\u5438\u6536\u76f8\uff09<\/span>\uff0c\u800c<\/span><\/sub>\u5219\u76f8\u53cd<\/span>\uff08\u5bf9\u5e94\u6d3b\u8dc3\u76f8\uff09<\/span>\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u5fae\u8c03\u63a7\u5236\u53c2\u6570<\/sub>\u4f7f\u5927\u8111\u5728<\/sub><\/span>\uff08\u7531\u03bdc<\/sub><\/span><\/span>\u5b9a\u4e49\u7684\u4e34\u754c\u70b9\uff09<\/span>\u5904OC\u3002\u5fae\u8c03\u4f9d\u8d56\u4e8e\u5916\u90e8\u673a\u5236\u64cd\u7eb5\u7684 <\/sub>\u3002<\/span><\/section>\n

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qC\u7684Langevin\u65b9\u7a0b <\/strong>\u4e3a\u4e86\u5bfc\u51fa\u5438\u6536\u76f8\u548c\u6d3b\u8dc3\u76f8\u7684qC\uff0c\u6211\u4eec\u8003\u8651\u4e0a\u8ff0\u516c\u5f0f\uff083,4\uff09\u7684\u5e73\u5747\u573a\u8fd1\u4f3c\uff0c<\/span><\/section>\n

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\uff085\uff09<\/span><\/section>\n
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\u57fa\u4e8e\u5e73\u5747\u573a\u5047\u8bbe\uff0c<\/span><\/sub>\u4f1a\u88ab\u5ffd\u7565\u3002\u5f53\u6ca1\u6709\u523a\u6fc0\u8f93\u5165\u3002\u5373<\/sub>\u65f6\uff0c\u6d3b\u8dc3\u548c\u5438\u6536\u76f8\u7684\u4e34\u754c\u70b9\u662f\u3002\u516c\u5f0f\uff085,6\uff09\u7684\u7a33\u5b9a\u89e3\u4e3a<\/span><\/section>\n

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\u5f53\u523a\u6fc0\u8f93\u5165\u53d8\u5f3a\uff0c\u4e0a\u8ff0\u7a33\u5b9a\u89e3\u4e0d\u5b58\u5728\u9664\u975e\u6ee1\u8db3<\/sub>\uff0c\u6b64\u65f6\u6211\u4eec\u53ef\u4ee5\u5bfc\u51fa<\/span><\/section>\n

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\u6b64\u65f6\uff0c\u4e34\u754c\u70b9<\/sub><\/span>\u4e0d\u4e00\u5b9a\u662f\u7a33\u6001\u3002\u9664\u975e\u5b58\u5728\u67d0\u4e9b\u7406\u60f3\u7684\u5916\u751f\u673a\u5236\uff0c\u6bcf\u5f53<\/span>\u589e\u52a0\u65f6\uff0c<\/span>\u6301\u7eed\u589e\u5927\uff0c\u5426\u5219\u795e\u7ecf\u52a8\u529b\u5b66\u7684\u5fae\u8c03\u65e0\u6cd5\u6d88\u9664<\/span>\u7684\u5f71\u54cd\u3002\u56e0\u6b64\uff0c\u5fae\u8c03\u8fc7\u7a0b\u53ef\u80fd\u53ea\u80fd\u4f7f\u5927\u8111\u5230\u8fbe\u795e\u7ecf\u52a8\u529b\u5b66\u654f\u611f\u6027\u76f8\u5bf9\u8f83\u5927\u7684\u51c6\u4e34\u754c\u533a\u57df\u3002\u6700\u521d\u7684OC\u6d88\u5931\u5e76\u88abqC\u53d6\u4ee3\u3002<\/span><\/section>\n

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SOC\u7684Langevin\u65b9\u7a0b <\/strong>\u4e3a\u4e86\u66f4\u51c6\u786e\u5730\u7406\u89e3SOC\u548cOC\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u8003\u8651<\/sub>\u4f7f\u5f97<\/sub><\/span>\uff08\u5373\u65f6\u95f4\u5c3a\u5ea6\u7684\u65e0\u9650\u5206\u79bb\uff09<\/span>\u3002\u56e0\u6b64\u516c\u5f0f\uff085,6\uff09\u7684\u7a33\u6001\u89e3\u53d8\u4e3a<\/span><\/section>\n

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SOqC\u7684Langevin\u65b9\u7a0b<\/strong> \u5bf9\u4e8eSOqC\uff0c\u975e\u96f6\u4f53\u8017\u6563\u6253\u7834\u4e86\u5b88\u6052\u5b9a\u5f8b\uff0c\u5728\u795e\u7ecf\u52a8\u529b\u5b66\u4e2d\u4ea7\u751f\u4e86\u975e\u9a6c\u5c14\u79d1\u592b\u5206\u91cf[20,30]\u3002\u5728\u7406\u60f3\u60c5\u51b5\u4e0b\uff0c\u8db3\u591f\u5927\u7684\u795e\u7ecf\u52a8\u529b\u5b66\u9a71\u52a8\u9879<\/span>\uff08\u5982\u523a\u6fc0\u8f93\u5165\uff09<\/span>\u4ee5\u4efb\u610f\u6162\u7684\u65f6\u95f4\u5c3a\u5ea6\u53d1\u751f<\/span>\uff08\u5373\u4ec5\u53d1\u751f\u5728\u795e\u7ecf\u96ea\u5d29\u4e4b\u95f4\u7684\u95f4\u9694\u5185\uff09<\/span>\uff0c\u5927\u8111\u8868\u73b0\u51fa\u7eaf\u7cb9\u7684\u52a8\u6001\u6e17\u900f\u884c\u4e3a[30]\u3002\u4e3a\u4e86\u7406\u89e3\u8fd9\u4e2a\u5c5e\u6027\uff0c\u8ba9\u6211\u4eec\u8003\u8651\u516c\u5f0f5\u548c6\u7684\u53d8\u4f53\uff0c\u5176\u4e2d\u8017\u6563\u9879<\/sub>\u4e0d\u53ef\u5ffd\u7565\uff0c<\/span><\/section>\n

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[1] Fontenele, A. J., de Vasconcelos, N. A., Feliciano, T., Aguiar, L. A., Soares-Cunha, C., Coimbra, B., \u2026 Copelli, M. (2019). Criticality between cortical states. Physical Review Letters<\/em>, 122(20), 208101.<\/span><\/section>\n
[2] Antonopoulos, C. G. (2016). Dynamic range in the C. elegans<\/em> brain network. Chaos: An Interdisciplinary Journal of Nonlinear Science<\/em>, 26(1), 013102.<\/span><\/section>\n
[3] Li, X., & Small, M. (2012). Neuronal avalanches of a self-organized neural network with active-neuron-dominant structure. Chaos: An Interdisciplinary Journal of Nonlinear<\/em><\/span><\/section>\n
[4] Shew, W. L., Yang, H., Yu, S., Roy, R., & Plenz, D. (2011). Information capacity and transmission are maximized in balanced cortical networks with neuronal avalanches. Journal of Neuroscience<\/em>, 31(1), 55\u201363.<\/span><\/section>\n
[5] Beggs, J. M., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of Neuroscience<\/em>, 23(35), 11167\u201311177.<\/span><\/section>\n
[6] Dalla Porta, L., & Copelli, M. (2019). Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic m\/eeg results. PLoS Computational Biology<\/em>, 15(4), e1006924.<\/span><\/section>\n
[7] Fosque, L. J., Williams-Garc\u00eda, R. V., Beggs, J. M., & Ortiz, G. (2021). Evidence for quasicritical brain dynamics. Physical Review Letters<\/em>, 126(9), 098101.<\/span><\/section>\n
[8] Fosque, L. J., Williams-Garc\u00eda, R. V., Beggs, J. M., & Ortiz, G. (2021). Evidence for quasicritical brain dynamics. Physical Review Letters<\/em>, 126(9), 098101.<\/span><\/section>\n
[9] Tka\u010dik, G., Mora, T., Marre, O., Amodei, D., Palmer, S. E., Berry, M. J., & Bialek, W. (2015). Thermodynamics and signatures of criticality in a network of neurons. Proceedings of the National Academy of Sciences<\/em>, 112(37), 11508\u201311513.<\/span><\/section>\n
[10] Gnesotto, F. S., Mura, F., Gladrow, J., & Broedersz, C. P. (2018). Broken detailed balance and non-equilibrium dynamics in living systems: A review. Reports on Progress in Physics<\/em>, 81(6), 066601.<\/span><\/section>\n
[11] Lynn, C. W., Cornblath, E. J., Papadopoulos, L., Bertolero, M. A., & Bassett, D. S. (2021). Broken detailed balance and entropy production in the human brain. Proceedings of the National Academy of Sciences<\/em>, 118(47), e2109889118.<\/span><\/section>\n
[12] Perl, Y. S., Bocaccio, H., Pallavicini, C., P\u00e9rez-Ipi\u00f1a, I., Laureys, S., Laufs, H., \u2026 Tagliazucchi, E. (2021). Nonequilibrium brain dynamics as a signature of consciousness. Physical Review E<\/em>, 104(1), 014411.<\/span><\/section>\n
[13] Stewart, C. V., & Plenz, D. (2006). Inverted-U profile of dopamine\u2013NMDA-mediated spontaneous avalanche recurrence in superficial layers of rat prefrontal cortex. Journal of Neuroscience<\/em>, 26(31), 8148\u20138159.<\/span><\/section>\n
[14] Stewart, C. V., & Plenz, D. (2008). Homeostasis of neuronal avalanches during postnatal cortex development in vitro. Journal of Neuroscience Methods<\/em>, 169(2), 405\u2013416.<\/span><\/section>\n
[15] Levina, A., Herrmann, J. M., & Geisel, T. (2007). Dynamical synapses causing self-organized criticality in neural networks. Nature Physics<\/em>, 3(12), 857\u2013860.<\/span><\/section>\n
[16] Chialvo, D. R. (2010). Emergent complex neural dynamics. Nature Physics<\/em>, 6(10), 744\u2013750.<\/span><\/section>\n
[17] Williams-Garc\u00eda, R. V., Moore, M., Beggs, J. M., & Ortiz, G. (2014). Quasicritical brain dynamics on a nonequilibrium Widom line.<\/span><\/section>\n
[18] Malcai, O., Shilo, Y., & Biham, O. (2006). Dissipative sandpile models with universal exponents. Physical Review E<\/em>, 73(5), 056125.<\/span><\/section>\n
[19] Bonachela, J. A., De Franciscis, S., Torres, J. J., & Mu\u00f1oz, M. A. (2010). Self-organization without conservation: Are neuronal avalanches generically critical? Journal of Statistical Mechanics: Theory and Experiment<\/em>, 2010(2), P02015.<\/span><\/section>\n
[20] Bonachela, J. A., & Mu\u00f1oz, M. A. (2009). Self-organization without conservation: True or just apparent scale-invariance? Journal of Statistical Mechanics: Theory and Experiment<\/em>, 2009(9), P09009.<\/span><\/section>\n
[21] Rubinov, M., Sporns, O., Thivierge, J.-P., & Breakspear, M. (2011). Neurobiologically realistic determinants of self-organized criticality in networks of spiking neurons. PLoS Computational Biology<\/em>, 7(6), e1002038.<\/span><\/section>\n
[22] De Arcangelis, L., Perrone-Capano, C., & Herrmann, H. J. (2006). Self-organized criticality model for brain plasticity. Physical Review Letters<\/em>, 96(2), 028107.<\/span><\/section>\n
[23] Girardi-Schappo, M., Galera, E. F., Carvalho, T. T., Brochini, L., Kamiji, N. L., Roque, A. C., & Kinouchi, O. (2021). A unified theory of E\/I synaptic balance, quasicritical neuronal avalanches and asynchronous irregular spiking. Journal of Physics: Complexity<\/em>, 2(4), 045001.<\/span><\/section>\n
[24] Ma, Z., Turrigiano, G. G., Wessel, R., & Hengen, K. B. (2019). Cortical circuit dynamics are homeostatically tuned to criticality in vivo. Neuron<\/em>, 104(4), 655\u2013664.<\/span><\/section>\n
[25] Larremore, D. B., Carpenter, M. Y., Ott, E., & Restrepo, J. G. (2012). Statistical properties of avalanches in networks. Physical Review E<\/em>, 85(6), 066131.<\/span><\/section>\n
[26] di Santo, S., Villegas, P., Burioni, R., & Mu\u00f1oz, M. A. (2018). Landau\u2013Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization. Proceedings of the National Academy of Sciences<\/em>, 115(7), E1356\u2013E1365.<\/span><\/section>\n
[27] Acebr\u00f3n, J. A., Bonilla, L. L., P\u00e9rez Vicente, C. J., Ritort, F., & Spigler, R. (2005). The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics<\/em>, 77, 137\u2013185.<\/span><\/section>\n
[28] Cocchi, L., Gollo, L. L., Zalesky, A., & Breakspear, M. (2017). Criticality in the brain: A synthesis of neurobiology, models and cognition. Progress in Neurobiology<\/em>, 158, 132\u2013152.<\/span><\/section>\n
[29] Girardi-Schappo, M. (2021). Brain criticality beyond avalanches: Open problems and how to approach them. Journal of Physics: Complexity<\/em>, 2(3), 031003.<\/span><\/section>\n
[30] Buend\u00eda, V., di Santo, S., Bonachela, J. A., & Mu\u00f1oz, M. A. (2020a). Feedback mechanisms for self-organization to the edge of a phase transition. Frontiers in Physics<\/em>, 8, 333.<\/span><\/section>\n
[31] Hinrichsen, H. (2000). Non-equilibrium critical phenomena and phase transitions into absorbing states. Advances in Physics<\/em>, 49(7), 815\u2013958.<\/span><\/section>\n
[32] Henkel, M., Hinrichsen, H., L\u00fcbeck, S., & Pleimling, M. (2008). Non-equilibrium phase transitions<\/em> (Vol. 1). Berlin, Germany: Springer.<\/span><\/section>\n
[33] Buend\u00eda, V., Villegas, P., Burioni, R., & Mu\u00f1oz, M. A. (2021). Hybrid-type synchronization transitions: Where incipient oscillations, scale-free avalanches, and bistability live together. Physical Review Research<\/em>, 3(2), 023224.<\/span><\/section>\n
[34] L\u00fcbeck, S. (2004). Universal scaling behavior of non-equilibrium phase transitions. International Journal of Modern Physics B<\/em>, 18(31n32), 3977\u20134118.<\/span><\/section>\n
[35] Clauset, A., Shalizi, C. R., & Newman, M. E. (2009). Power-law distributions in empirical data. SIAM Review<\/em>, 51(4), 661\u2013703.<\/span><\/section>\n
[36] Virkar, Y., & Clauset, A. (2014). Power-law distributions in binned empirical data. The Annals of Applied Statistics<\/em>, 8(1), 89\u2013119.<\/span><\/section>\n
[37] Marshall, N., Timme, N. M., Bennett, N., Ripp, M., Lautzenhiser, E., & Beggs, J. M. (2016). Analysis of power laws, shape collapses, and neural complexity: New techniques and MATLAB support via the NCC toolbox. Frontiers in Physiology<\/em>, 7, 250.<\/span><\/section>\n


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\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


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1. <\/strong>\u5927\u8111\u52a8\u529b\u5b66\u5bf9\u79f0\u6027\u7834\u7f3a\u4e0e\u610f\u8bc6\u72b6\u6001\u53d7\u635f<\/a><\/strong><\/span><\/section>\n
2.<\/strong> \u957f\u6587\u7efc\u8ff0\uff1a\u5927\u8111\u4e2d\u7684\u71b5\u3001\u81ea\u7531\u80fd\u3001\u5bf9\u79f0\u6027\u548c\u52a8\u529b\u5b66<\/a><\/strong><\/span><\/strong><\/section>\n
3.<\/strong> \u524d\u6cbf\u7efc\u8ff0\uff1a\u5927\u8111\u590d\u6742\u81ea\u9002\u5e94\u52a8\u529b\u5b66\u7684\u795e\u7ecf\u8c03\u8282\u63a7\u5236<\/a><\/strong><\/strong><\/span><\/section>\n
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6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n

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