Generalized Forced Van Der Pol Oscillator Phase Plot
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Hello,
I am trying to write a program to solve a forced van der pol oscillator and give its phase plot. I found a code on these forums, posted by @KSSV that solved an unforced van der pol oscillator and I just added a forcing term, and it worked. Here is the code
function VanderPol()
[t,y] = ode23(@vdp1,[0 20],[2; 0]);
plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution of van der Pol Equation (\mu = 1) with ODE23');
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2')
figure
plot(y(:,1),y(:,2))
title('Phase plane plot')
end
function dydt = vdp1(t,y)
dydt = [y(2); 3*(1-y(1)^2)*y(2)-y(1)+8*sin(4*t)];
end
I was able to go in and play with the variables to obtain different results, which was great, but ideally I would want to generalize the code such that the second line read
[t,y] = ode23(@vdp1,[0 20],[idis; ivel]);
And the line prior to end read
dydt=[y(2); mu*(1-y(1)^2)*y(2)-y(1)+A*sin(omega*t)];
And then be able to call VanderPol(idis, idel, mu, A, omega) and be able to solve that without having to go in and manually change it each time
采纳的回答
Star Strider
2020-4-17
Try this:
function [t,y] = VanderPol(idis, ivel, mu, A, omega)
[t,y] = ode23(@vdp1,[0 20],[2; 0]);
plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution of van der Pol Equation (\mu = 1) with ODE23');
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2')
figure
plot(y(:,1),y(:,2))
title('Phase plane plot')
function dydt = vdp1(t,y)
dydt = [y(2); mu*(1-y(1)^2)*y(2)-y(1)+A*sin(omega*t)];
end
end
Then to call it:
idis = 2;
ivel = 0;
A = 8;
omega = 4;
mu = 3;
[t,y] = VanderPol(idis, ivel, mu, A, omega);
figure
plot(t,y)
grid
I added a tweak so that you can get the integrated results from your funciton. It is otherwise what you wrote.
.
3 个评论
Thomas Ward
2020-4-17
Star Strider
2020-4-17
As always, my pleasure!
george korris
2021-4-15
hey guys is this code solving this equation: 
and what does: Solution of van der Pol Equation (\mu = 1) with ODE23' that the first figure has as title mean?
and what does: Solution of van der Pol Equation (\mu = 1) with ODE23' that the first figure has as title mean?更多回答（0 个）
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