How to plot a vector map for a differential system(in ode45) with a switch condition ?

% y is output from ode45

[gridx1,gridy1]=meshgrid(logspace(thetamin,thetamax,length(y(1:fix(end/2),1))),logspace(thetadotmin,thetadotmax,length(thetadot(1:fix(end/2),2))));

quiver(y(1:fix(end/2),1), y(1:fix(end/2),2),gridx1,gridy1);%Only plotted the first half of the output to avoid the even higher frequency areas and used logspace in place of linspace to avoid hanging my laptop

I wish to plot a vector map for a switching system along the switching surface h. So far, I tried quiver, which just hangs my laptop when the high frequency switching condition occurs.

Example problem:

[KSSV]

Why don't you show us your full code?

[Vignesh Ramakrishnan]

Sorry, I can't. I should've posted a toy problem instead. Also, the code has a lot of event triggers etc which would take away the focus from my main problem here i.e. scaling.

Answer 1

[Sam Chak]

Hi @Vignesh Ramakrishnan

Since you didn't provide the code, the following involves some guesswork in an attempt to reproduce/duplicate your graph.

The simplest form of is probably a additive function, and so I've tried . But, your scale at is relatively small.

k = 0;
fv1 = @(t, x, y) y;
fv2 = @(t, x, y) k*sin(t) + 5.2*sign(-((4/10)*x + y));
opt = odeset('RelTol', 1e-4, 'AbsTol', 1e-6);
[t, v] = ode45(@(t, x) ([fv1(t, x(1), x(2)); fv2(t, x(1), x(2))]), [0 20], [10 0], opt);

Next is plotting.

subplot(2,1,1)
plot(t, v(:,1), 'linewidth', 1.5)

subplot(2,1,2)
plot(v(:,1), v(:,2), 'linewidth', 1.5)
hold on

And then the quiver plot is added.

[X, Y] = meshgrid(0:10/14:10, -4:4/7:0);    % Do NOT make very fine mesh partitions
U = Y;
V = 5.2*sign(-((4/10)*X + Y));
quiver(X, Y, U, V, 0.5)

I'll let the Experts to handle your case for , which indicates an non-autonomous system. Probably require quiver3() to show the evolution of the direction field in 3D as the system response is propagated forward in time t, as demonstrated by Dr. @Star Strider in this solution:

https://www.mathworks.com/matlabcentral/answers/336259-time-series-with-quiver

[Vignesh Ramakrishnan]

Thanks @Sam Chak