如何绘制范德波尔振荡器的方向场? [英] How to draw the direction field of van der pol oscillator?

问题描述

我正在尝试获取此Wiki页面上显示的方向场和相像:

I am trying to get the direction field and phase portrait shown on this wiki page:

维基百科中的Van der Pol振荡器

我的代码:

options = odeset('MaxStep',0.5);
temp = inputdlg('Enter mu value');
mu = str2double(temp{1,1});
[t,y] = ode45(@(t,y) vdp1_1(t,y,mu),[0 10],[2; 0],options);
plot(y(:,1),y(:,2));
hold on
quiver(y(:,1), y(:,2), gradient(y(:,1)), gradient(y(:,2) ))
hold off

function dydt = vdp1_1(t,y,mu)
    dydt = zeros(2,1);
    dydt(1) = y(2);
    dydt(2) = [mu * (1-y(1)^2)*y(2)-y(1)];
end

电流输出:

所需的输出: 如何获得方向字段的顶部，如Wiki页面图

Desired Output: How to get the direction field on top of this as shown in the wiki page figure

谢谢，
戈皮

推荐答案

您需要在要显示箭头的每个点上计算矢量场.然后用颤动器绘制该图.例如.

You need to calculate the vector field at every point you want an arrow to be shown. And then you plot this with quiver. For example.

[Xs,Ys]=meshgrid(-5:5,-5:5); % Will define the positions where we want to plot

Us=Ys; % From your equations, these are the values of the field at each point
Vs=mu*(1-Xs.^2).*Ys-Xs;

quiver(Xs,Ys,Us,Vs) % Should plot the field you want, just add the trajectory on top

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