{"id":7549,"date":"2024-07-19T07:01:03","date_gmt":"2024-07-18T23:01:03","guid":{"rendered":""},"modified":"2024-07-19T07:01:03","modified_gmt":"2024-07-18T23:01:03","slug":"\u975e\u7ebf\u6027\u7cfb\u7edf\u6982\u5ff5_\u975e\u7ebf\u6027\u7684\u6982\u5ff5\u662f\u4ec0\u4e48","status":"publish","type":"post","link":"https:\/\/mushiming.com\/7549.html","title":{"rendered":"\u975e\u7ebf\u6027\u7cfb\u7edf\u6982\u5ff5_\u975e\u7ebf\u6027\u7684\u6982\u5ff5\u662f\u4ec0\u4e48"},"content":{"rendered":"

\n <\/path> \n<\/svg> <\/p>\n

\u975e\u7ebf\u6027\u7cfb\u7edf\u7406\u8bba\uff08\u7b2c\u4e8c\u7248\uff09\u4f5c\u8005\uff1a\u65b9\u52c7\u7eaf \u5362\u6842\u7ae0<\/h2>\n

\u7b2c\u4e00\u7ae0 \u975e\u7ebf\u6027\u7cfb\u7edf\u4ecb\u7ecd<\/p>\n

\n
\n

\u6587\u7ae0\u76ee\u5f55<\/h4>\n
    \n
  • \u975e\u7ebf\u6027\u7cfb\u7edf\u7406\u8bba\uff08\u7b2c\u4e8c\u7248\uff09\u4f5c\u8005\uff1a\u65b9\u52c7\u7eaf \u5362\u6842\u7ae0<\/li>\n
  • \u524d\u8a00<\/li>\n
  • \u4e00\u3001\u603b\u7ed3<\/li>\n
  • \n
      \n
    • 1.\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027<\/li>\n
    • 2.\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7279\u6027<\/li>\n
    • 3.\u5e38\u89c1\u7684\u975e\u7ebf\u6027\u7cfb\u7edf\u8bbe\u8ba1\u4e0e\u5206\u6790\u65b9\u6cd5<\/li>\n<\/ul>\n<\/li>\n
    • \u4e8c\u3001\u8bfe\u540e\u4e60\u9898<\/li>\n
    • \n
        \n
      • 4.<\/li>\n
      • 5.<\/li>\n
      • 6.<\/li>\n<\/ul>\n<\/li>\n
      • \u603b\u7ed3<\/li>\n<\/ul>\n<\/div>\n
        \n

        \u524d\u8a00<\/h2>\n

        \u770b\u5b8c\u7b2c\u4e00\u7ae0\uff0c\u5199\u4e00\u70b9\u603b\u7ed3\u548c\u8bfe\u540e\u4e60\u9898\uff0c\u672c\u4eba\u975e\u63a7\u5236\u4e13\u4e1a\uff0c\u53ea\u662f\u4e2a\u4eba\u7231\u597d\uff0c\u5982\u6709\u95ee\u9898\uff0c\u8bf7\u591a\u6307\u6559<\/p>\n

        \n

        \u4e00\u3001\u603b\u7ed3<\/h2>\n

        1.\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027<\/h3>\n
          \n
        • \u7ebf\u6027\u7cfb\u7edf\uff1a
          \u6ee1\u8db3\u9f50\u6b21\u6027\u548c\u53e0\u52a0\u6027
          \u53ef\u5229\u7528\u4f20\u51fd\u548c\u72b6\u6001\u7a7a\u95f4\u65b9\u7a0b\u8868\u793a
          \u7a33\u5b9a\u6027\u5b8c\u5168\u53d6\u51b3\u4e8e\u7cfb\u7edf\u7684\u7ed3\u6784\u548c\u53c2\u6570\uff08\u4f20\u51fd\u7684\u95ed\u73af\u6781\u70b9\/\u72b6\u6001\u7a7a\u95f4\u7684\u7cfb\u7edf\u77e9\u9635\uff09\uff0c\u4e0e\u7cfb\u7edf\u7684\u521d\u59cb\u72b6\u6001\u65e0\u5173
          \u7a33\u5b9a\u6027\u5efa\u7acb\u5728\u5168\u5c40\u610f\u4e49\u4e0a<\/li>\n
        • \u975e\u7ebf\u6027\u7cfb\u7edf\uff1a
          \u4e0d\u6ee1\u8db3\u9f50\u6b21\u6027\u548c\u53e0\u52a0\u6027
          \u7a33\u5b9a\u6027\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u7cfb\u7edf\u7684\u7ed3\u6784\u548c\u53c2\u6570\uff0c\u540c\u65f6\u4e5f\u548c\u7cfb\u7edf\u7684\u521d\u59cb\u72b6\u6001\u76f4\u63a5\u5173\u7cfb
          \u7a33\u5b9a\u6027\u8fd8\u533a\u5206\u4e3a\u5168\u5c40\u8fd8\u662f\u5c40\u90e8<\/li>\n<\/ul>\n

          2.\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7279\u6027<\/h3>\n
            \n
          • \u591a\u5e73\u8861\u70b9
            \u7cfb\u7edf\u5177\u6709\u591a\u4e2a\u5e73\u8861\u70b9<\/li>\n
          • \u6781\u9650\u73af
            \u975e\u7ebf\u6027\u7cfb\u7edf\u5728\u65e0\u5916\u529b\u4f5c\u7528\u4e0b\u5448\u73b0\u51fa\u4e00\u79cd\u56fa\u6709\u9891\u7387\u548c\u56fa\u6709\u632f\u5e45\u7684\u7b49\u5e45\u9707\u8361
            \u662f\u7cfb\u7edf\u672c\u8eab\u7279\u6027\uff0c\u4e0e\u7cfb\u7edf\u8f93\u5165\u65e0\u5173<\/li>\n
          • \u6df7\u6c8c
            \u5bf9\u4e8e\u975e\u7ebf\u6027\u7cfb\u7edf\u800c\u8a00\uff0c\u5176\u8f93\u51fa\u5bf9\u521d\u59cb\u6761\u4ef6\u53d8\u5316\u6781\u5176\u654f\u611f<\/li>\n
          • \u78c1\u6ede
            \u7cfb\u7edf\u7684\u8f93\u51fa\u503c\u4e0d\u4ec5\u53d6\u51b3\u4e8e\u5f53\u524d\u7684\u8f93\u5165\u91cf\uff0c\u8fd8\u4e0e\u8f93\u5165\u91cf\u53d8\u5316\u8d8b\u52bf\u6709\u5173<\/li>\n
          • \u9971\u548c<\/li>\n<\/ul>\n

            3.\u5e38\u89c1\u7684\u975e\u7ebf\u6027\u7cfb\u7edf\u8bbe\u8ba1\u4e0e\u5206\u6790\u65b9\u6cd5<\/h3>\n
              \n
            • \u76f8\u5e73\u9762\u5206\u6790\u6cd5
              \u53ea\u9002\u7528\u4e8e\u4e8c\u9636\u7cfb\u7edf<\/li>\n
            • \u63cf\u8ff0\u51fd\u6570\u6cd5<\/li>\n
            • \u674e\u96c5\u666e\u8bfa\u592b\u6cd5
              \u76f4\u63a5\u6cd5\u548c\u95f4\u63a5\u6cd5<\/li>\n<\/ul>\n

              \u4e8c\u3001\u8bfe\u540e\u4e60\u9898<\/h2>\n

              4.<\/h3>\n

              \u5df2\u77e5\u975e\u7ebf\u6027\u7cfb\u7edf\u52a8\u6001\u7279\u6027\u5982\u4e0b\uff1a
              x \u02d9 \u2009\u2009 = \u2009\u2009 \u2212 x + x 3 \\dot{x}\\,\\,=\\,\\,-x+x^3 <\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
              \u8bd5\u6c42\u51fa\u7cfb\u7edf\u7684\u6240\u6709\u5e73\u8861\u70b9\u5e76\u7b80\u7565\u5206\u6790\u5176\u7a33\u5b9a\u6027
              \u2235 x \u02d9 \u2009\u2009\u2009 = \u2009\u2009 \u2212 x + x 3 = \u2212 x ( x 2 \u2212 1 ) \u2234 { x \u02d9 \u2009 > 0 , x > 1 x \u02d9 \u2009 < 0 , 0 < x < 1 x \u02d9 \u2009 > 0 , \u2212 1 < x < 0 x \u02d9 \u2009 < 0 , x < \u2212 1 \\because \\dot{x}\\,\\,\\,=\\,\\,-x+x^3=-x\\left( x^2-1 \\right) \\\\ \\therefore \\begin{cases} \\dot{x}\\,>0,x>1\\\\ \\dot{x}\\,<0,0<x<1\\\\ \\dot{x}\\,>0,-1<x<0\\\\ \\dot{x}\\,<0,x<-1\\\\ \\end{cases} <\/span><\/span>\u2235<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>(<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>\u2234<\/span><\/span><\/span><\/span><\/span>\u23a9<\/span><\/span><\/span><\/span>
              \n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u23a8<\/span><\/span><\/span><\/span>
              \n \n <\/path> \n <\/svg><\/span><\/span><\/span>\u23a7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span>0<\/span>,<\/span><\/span>x<\/span><\/span>><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span>0<\/span>,<\/span><\/span>0<\/span><\/span><<\/span><\/span>x<\/span><\/span><<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>><\/span><\/span>0<\/span>,<\/span><\/span>\u2212<\/span>1<\/span><\/span><<\/span><\/span>x<\/span><\/span><<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span>0<\/span>,<\/span><\/span>x<\/span><\/span><<\/span><\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u53ef\u4ee5\u5f97\u5230\uff1a
              i f \u2009\u2009 x > 1 , x \u2197 \u27f6 \u221e \u2009\u2009 i f \u2009\u2009 0 < x < 1 , x \u2198 \u27f6 0 \u2009\u2009 i f \u2009\u2009 \u2212 1 < x < 0 , x \u2197 \u27f6 0 \u2009\u2009 i f \u2009\u2009 x < \u2212 1 , x \u2198 \u27f6 \u2212 \u221e \u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u5230\uff0c\u5f53 \u2212 1 < x < 1 \u65f6\uff0c x \u4f1a\u8d8b\u8fd1\u4e8e 0 , \u662f\u5e73\u8861\u70b9 \u6b64\u5916\uff0c\u5f53 x = \u00b1 1 \u65f6\uff0c x \u02d9 \u2009 = 0 \uff0c\u4e5f\u4f1a\u7a33\u5b9a if\\,\\,x>1 , x\\nearrow \\longrightarrow \\infty \\\\ \\,\\, if\\,\\,0<x<1 ,x\\searrow \\longrightarrow 0 \\\\ \\,\\, if\\,\\,-1<x<0,x\\nearrow \\longrightarrow 0 \\\\ \\,\\, if\\,\\,x<-1,x\\searrow \\longrightarrow -\\infty \\\\ \\text{\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u5230\uff0c\u5f53}-1<x<1\\text{\u65f6\uff0c}x\\text{\u4f1a\u8d8b\u8fd1\u4e8e}0,\\text{\u662f\u5e73\u8861\u70b9} \\\\ \\text{\u6b64\u5916\uff0c\u5f53}x=\\pm 1\\text{\u65f6\uff0c}\\dot{x}\\,=0\\text{\uff0c\u4e5f\u4f1a\u7a33\u5b9a} <\/span><\/span>i<\/span>f<\/span><\/span><\/span>x<\/span><\/span>><\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>x<\/span><\/span>\u2197\u27f6<\/span><\/span><\/span><\/span>\u221e<\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>f<\/span><\/span><\/span>0<\/span><\/span><<\/span><\/span><\/span><\/span>x<\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span>,<\/span><\/span>x<\/span><\/span>\u2198\u27f6<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>f<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><<\/span><\/span><\/span><\/span>x<\/span><\/span><<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>x<\/span><\/span>\u2197\u27f6<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>f<\/span><\/span><\/span>x<\/span><\/span><<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>,<\/span><\/span>x<\/span><\/span>\u2198\u27f6<\/span><\/span><\/span><\/span>\u2212<\/span>\u221e<\/span><\/span><\/span><\/span>\u7efc\u4e0a\uff0c\u53ef\u4ee5\u5f97\u5230\uff0c\u5f53<\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><<\/span><\/span><\/span><\/span>x<\/span><\/span><<\/span><\/span><\/span><\/span>1<\/span>\u65f6\uff0c<\/span><\/span>x<\/span>\u4f1a\u8d8b\u8fd1\u4e8e<\/span><\/span>0<\/span>,<\/span><\/span>\u662f\u5e73\u8861\u70b9<\/span><\/span><\/span><\/span><\/span>\u6b64\u5916\uff0c\u5f53<\/span><\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u00b1<\/span>1<\/span>\u65f6\uff0c<\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>\uff0c\u4e5f\u4f1a\u7a33\u5b9a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
              \u5176\u5b9e\uff0c\u6839\u636e\u4e4b\u524d\u6240\u5b66\uff0c\u53ef\u4ee5\u5229\u7528\u76f8\u5e73\u9762\u6cd5\u53ca\u8fdb\u884c\u5206\u6790
              \u6211\u4eec\u53ef\u4ee5\u6c42\u5f97 f ( x ) \u2009\u2009 = \u2009\u2009 x \u02d9 \u2009\u2009 = \u2009\u2009 \u2212 x + x 3 \u2009 \u7684\u96f6\u70b9 x 1 = 1 ; x 2 = \u2212 1 ; x 3 = 0 \u5728\u8fd9\u4e09\u4e2a\u70b9\u9644\u8fd1\u4f5c\u4e3a\u4e3a\u521d\u59cb\u70b9\u8fdb\u884c\u5206\u6790 \\text{\u6211\u4eec\u53ef\u4ee5\u6c42\u5f97}f\\left( x \\right) \\,\\,=\\,\\,\\dot{x}\\,\\,=\\,\\,-x+x^3\\,\\text{\u7684\u96f6\u70b9} \\\\ x_1=1;x_2=-1;x_3=0 \\\\ \\text{\u5728\u8fd9\u4e09\u4e2a\u70b9\u9644\u8fd1\u4f5c\u4e3a\u4e3a\u521d\u59cb\u70b9\u8fdb\u884c\u5206\u6790} <\/span><\/span>\u6211\u4eec\u53ef\u4ee5\u6c42\u5f97<\/span><\/span>f<\/span><\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u7684\u96f6\u70b9<\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>;<\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>1<\/span>;<\/span><\/span>x<\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u5728\u8fd9\u4e09\u4e2a\u70b9\u9644\u8fd1\u4f5c\u4e3a\u4e3a\u521d\u59cb\u70b9\u8fdb\u884c\u5206\u6790<\/span><\/span><\/span><\/span><\/span><\/span><\/span>
              \u7ed8\u5236\u76f8\u56fe\u51fd\u6570<\/p>\n

              %% \u7ed8\u5236\u76f8\u56fe<\/span> clc;<\/span>clear;<\/span>close all;<\/span> %% \u5b9a\u4e49\u5fae\u5206\u65b9\u7a0b<\/span> example_ode =<\/span> @<\/span>(<\/span>t,<\/span>x)<\/span> -<\/span>x+<\/span>x^<\/span>3<\/span>;<\/span> % \u5b9a\u4e49\u65f6\u95f4\u8303\u56f4<\/span> tspan =<\/span> [<\/span>0<\/span> 100<\/span>]<\/span>;<\/span> % \u521d\u59cb\u6761\u4ef6<\/span> x0 =<\/span> 0<\/span>;<\/span> % \u89e3\u5fae\u5206\u65b9\u7a0b<\/span> [<\/span>t,<\/span> x]<\/span> =<\/span> ode45<\/span>(<\/span>example_ode,<\/span> tspan,<\/span> x0)<\/span>;<\/span> for<\/span> i<\/span> =<\/span> 1<\/span>:<\/span>size<\/span>(<\/span>t)<\/span> dx<\/span>(<\/span>i<\/span>)<\/span> =<\/span> example_ode<\/span>(<\/span>t<\/span>(<\/span>i<\/span>)<\/span>,<\/span>x<\/span>(<\/span>i<\/span>)<\/span>)<\/span>;<\/span> end<\/span> % \u7ed8\u5236\u76f8\u56fe<\/span> figure;<\/span> plot<\/span>(<\/span>x,<\/span> dx,<\/span> 'LineWidth'<\/span>,<\/span> 2<\/span>)<\/span>;<\/span> xlabel<\/span>(<\/span>'x_1'<\/span>)<\/span>;<\/span> ylabel<\/span>(<\/span>'x_2'<\/span>)<\/span>;<\/span> title<\/span>(<\/span>'Phase Plot'<\/span>)<\/span>;<\/span> grid on;<\/span> <\/code><\/pre>\n
              \u56fe\u7247\u592a\u591a\uff0c\u8fd9\u91cc\u5c31\u4e0d\u653e\u4e86\uff0c\u8bfb\u8005\u53ef\u4ee5\u81ea\u5df1\u8fd0\u7528\u4ee3\u7801\u7ed8\u5236<\/p>\n
              5.<\/h3>\n
              \u5bf9\u4e8e\u5982\u4e0b\u975e\u7ebf\u6027\u7cfb\u7edf\uff1a
                x \u02d9 \u2009\u2009\u2009 = \u2009\u2009 \u2212 x + x 2 \\dot{x}\\,\\,\\,=\\,\\,-x+x^2 <\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
               \u5728\u521d\u59cb\u6761\u4ef6\u4e3a0.5\u548c0.2\u65f6\u7684\u54cd\u5e94\u66f2\u7ebf<\/p>\n
              \n
              \u89e3\u7b54\u4ee3\u7801\u5982\u4e0b<\/p>\n<\/blockquote>\n
              %% \u4e60\u98981-5<\/span> clc;<\/span>clear;<\/span>close all;<\/span> %% \u5b9a\u4e49\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u5fae\u5206\u65b9\u7a0b<\/span> nonlinear_system =<\/span> @<\/span>(<\/span>t,<\/span>x)<\/span> -<\/span>x+<\/span>x^<\/span>2<\/span>;<\/span> % \u8bbe\u7f6e\u521d\u59cb\u6761\u4ef6<\/span> initial_conditions =<\/span> [<\/span>0.5<\/span> 2<\/span>]<\/span>;<\/span> % \u4eff\u771f\u4e0d\u540c\u521d\u59cb\u6761\u4ef6\u4e0b\u7684\u7cfb\u7edf\u54cd\u5e94<\/span> for<\/span> i<\/span> =<\/span> 1<\/span>:<\/span>2<\/span> % \u8bbe\u7f6e\u5f53\u524d\u7684\u521d\u59cb\u6761\u4ef6<\/span> x0 =<\/span> initial_conditions<\/span>(<\/span>i<\/span>)<\/span>;<\/span> % \u8c03\u7528ode45\u6c42\u89e3\u5668<\/span> [<\/span>t,<\/span> x]<\/span> =<\/span> ode45<\/span>(<\/span>nonlinear_system,<\/span> [<\/span>0<\/span> 10<\/span>]<\/span>,<\/span> x0)<\/span>;<\/span> % \u7ed8\u5236\u54cd\u5e94\u66f2\u7ebf<\/span> subplot<\/span>(<\/span>1<\/span>,<\/span> 2<\/span>,<\/span> i<\/span>)<\/span>;<\/span> plot<\/span>(<\/span>t,<\/span> x)<\/span>;<\/span> title<\/span>(<\/span>sprintf<\/span>(<\/span>'Initial Condition: %d'<\/span>,<\/span> x0)<\/span>)<\/span>;<\/span> xlabel<\/span>(<\/span>'time'<\/span>)<\/span>;<\/span> ylabel<\/span>(<\/span>'State'<\/span>)<\/span>;<\/span> legend<\/span>(<\/span>'x1'<\/span>)<\/span>;<\/span> end<\/span> <\/code><\/pre>\n
              6.<\/h3>\n
              \u5bf9\u4e8e\u5982\u4e0b\u975e\u7ebf\u6027\u7cfb\u7edf\uff1a
                x \u02d9 \u2009\u2009\u2009 = \u2009\u2009 ( x \u2212 sin \u2061 x ) u \\dot{x}\\,\\,\\,=\\,\\,\\left( x-\\sin x \\right) u <\/span><\/span><\/span>x<\/span><\/span><\/span>\u02d9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>\u2212<\/span><\/span>sin<\/span><\/span>x<\/span>)<\/span><\/span><\/span>u<\/span><\/span><\/span><\/span><\/span><\/span>
               \u8bbe\u8ba1\u7684\u975e\u7ebf\u6027\u63a7\u5236\u5668\u4e3a\uff1a
                u = \u2212 x ( x \u2212 sin \u2061 x ) u=-x\\left( x-\\sin x \\right) <\/span><\/span>u<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>x<\/span><\/span>(<\/span>x<\/span><\/span>\u2212<\/span><\/span>sin<\/span><\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n
              \u5728\u521d\u59cb\u6761\u4ef6\u4e3a1\u65f6\u7684\u54cd\u5e94\u66f2\u7ebf<\/p>\n
              \n
              \u89e3\u7b54\u4ee3\u7801\u5982\u4e0b<\/p>\n<\/blockquote>\n
              %% \u4e60\u98981-6<\/span> clc;<\/span>clear;<\/span>close all;<\/span> %% \u5b9a\u4e49\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u5fae\u5206\u65b9\u7a0b<\/span> nonlinear_system =<\/span> @<\/span>(<\/span>t,<\/span>x)<\/span> -<\/span>x*<\/span>(<\/span>x-<\/span>sin<\/span>(<\/span>x)<\/span>)<\/span>^<\/span>2<\/span>;<\/span> % \u8bbe\u7f6e\u521d\u59cb\u6761\u4ef6<\/span> initial_conditions =<\/span> 1<\/span>;<\/span> % \u8bbe\u7f6e\u5f53\u524d\u7684\u521d\u59cb\u6761\u4ef6<\/span> x0 =<\/span> initial_conditions;<\/span> % \u8c03\u7528ode45\u6c42\u89e3\u5668<\/span> [<\/span>t,<\/span> x]<\/span> =<\/span> ode45<\/span>(<\/span>nonlinear_system,<\/span> [<\/span>0<\/span> 00<\/span>]<\/span>,<\/span> x0)<\/span>;<\/span> % \u7ed8\u5236\u54cd\u5e94\u66f2\u7ebf<\/span> plot<\/span>(<\/span>t,<\/span> x)<\/span>;<\/span> title<\/span>(<\/span>sprintf<\/span>(<\/span>'Initial Condition: %d'<\/span>,<\/span> x0)<\/span>)<\/span>;<\/span> xlabel<\/span>(<\/span>'time'<\/span>)<\/span>;<\/span> ylabel<\/span>(<\/span>'State'<\/span>)<\/span>;<\/span> legend<\/span>(<\/span>'x1'<\/span>)<\/span>;<\/span> <\/code><\/pre>\n
              \u603b\u7ed3<\/h2>\n","protected":false},"excerpt":{"rendered":"\u975e\u7ebf\u6027\u7cfb\u7edf\u6982\u5ff5_\u975e\u7ebf\u6027\u7684\u6982\u5ff5\u662f\u4ec0\u4e48\u975e\u7ebf\u6027\u7cfb\u7edf\u7406\u8bba_\u975e\u7ebf\u6027\u7cfb\u7edf\u7406\u8bba\u65b9\u52c7\u7eafpdf","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/7549"}],"collection":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/comments?post=7549"}],"version-history":[{"count":0,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/posts\/7549\/revisions"}],"wp:attachment":[{"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/media?parent=7549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/categories?post=7549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mushiming.com\/wp-json\/wp\/v2\/tags?post=7549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}