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参数拟合

求能将给定数据最佳拟合至范德波尔（Van der Pol）方程的参数 .

Wolfram Language code: peqns = {x''[t] - μ(1 - x[t] ^ 2)x'[t] + x[t] == 0, x[0] == 2, x'[0] == 0}; data = NDSolveValue[peqns /. μ -> 1., Table[{t, x[t] + RandomReal[{-.3, .3}]}, {t, 0, 10, .2}], {t, 10}];
Wolfram Language code: ListPlot[data, PlotRange -> All, PlotStyle -> Red, ImageSize -> Medium]
创建一个 ParametricFunction 对象并在 FindFit 中使用：
Wolfram Language code: pfun = ParametricNDSolveValue[{x''[t] - μ(1 - x[t] ^ 2)x'[t] + x[t] == 0, x[0] == 2, x'[0] == 0}, x, {t, 0, 10}, {μ}];
Wolfram Language code: fit = FindFit[data, pfun[μ][t], {{μ, 2}}, t]
Wolfram Language code: Show[ListPlot[data, PlotStyle -> Red], Plot[pfun[μ][t] /. fit, {t, 0, 10}], ImageSize -> Medium]