Vanderpol 的时间响应图、相图和poincare映射图Matlab实现

%张琪昌：《分岔与混沌理论及应用》P.46

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9Jt|)a;AyRqkj0% Author: Thomas Lee振动资讯&} c0JC_!`"J

% E-mail: lixf1979@126.com振动资讯S]ky3p~a4N

% Corresponding: School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China振动资讯7lh3r{b&P

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function xdot=van(t,y,flag,u,x0,w0,v,w)

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xdot=[y(2);振动资讯 wd"P#a.Q$\

u*(x0^2-y(1)^2)*y(2)-y(1)*w0^2-v*cos(w*t)];振动资讯7]}-|9n"HX
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u=[0.85,1.02,0.66,1.08];

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x0=1;w0=1;v=1;w=0.44;T=2*pi/w;

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str{1}='1';

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str{2}='2';

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str{3}='3';振动资讯q j_xSo5rW

str{4}='4';振动资讯1jl~.A]}

for j=1:4振动资讯"V(Vh
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    [t,y]=ode23('van',[0:T/100:10*T],[4,4],[],u(j),x0,w0,v,w);

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    figure振动资讯t&JF%w`:e$e1`2j

    subplot(2,1,1)

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    plot(t,y(:,1));

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    title('weiyiquxian');

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    xlabel('t');ylabel('x');

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    振动资讯C+z:M`r"un

    subplot(2,2,3)振动资讯[7wK:p/FQ

    plot(y(300:end,1),y(300:end,2));振动资讯3Z#H%`x!JK
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    axis([-3 3 -4 4]);振动资讯4CwP8I-\7rG8cO

    xlabel('x');ylabel('dx/dt');振动资讯%U"m)`$U~@

    title('xiangtu');

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    振动资讯:Qtj*w:z.A8e|j
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    subplot(2,2,4)振动资讯3p.z7fr FA['`#w%ph j

    axis([-3 1 -1 1])振动资讯y7lA9? he;f/Ar

    hold on振动资讯oc M"xG6c Q$P

    for i=500:100:1000

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        plot(y(i,1),y(i,2),'b.');振动资讯&UA,d_X:p4N

    end

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    title(str{j});

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end振动资讯R tC2mvd%V