Plotting system of differential equations

Hi,

does anybody know the code to plot a system of differential equations? For example say,

x1(dot) = -x2 + (x1)^2 -(x1*x2)

x2(dot) = x1 + (x1*x2)

Thanks in advance! :)

Sajith.

Answer 1

[Star Strider]

Yes.

Use ode45 to integrate your equations, then plot the solution.

Give it a go. It should be very easy for you to cast your system of equations as an Anonymous Function. If you have problems with your code, we can help you get it running.

[Sajith Dharmasena]

I'm not very familiar with MATLAB. Do you think you could show me how to use ode45 and then plot the functions?

Sajith

[Star Strider]

Since you already Accepted my Answer, here you go:

odesys = @(t,x) [(-x(2) + (x(1)).^2 -(x(1).*x(2))); (x(1) + 
(x(1).*x(2)))];
x0   = [0; 1];                          % Initial Conditions
tspan = [0 60];                         % Time Of Integration
[t, x] = ode45(odesys, tspan, x0);      % Integrate

figure(1)
plot(t, x)
grid
legend('x_1(t)', 'x_2(t)', 'Location', 'NE')

You didn’t specify time span (‘tspan’) or initial conditions (‘x0’), so you may want to revisit those, and specify different values.

[Sajith Dharmasena]

Thank you so much for your help!

[Sajith Dharmasena]

How do you plot x1 vs x2? (phase plane)

[Star Strider]

You plot just that:

plot(x(:,1), x(:,2))