MATLAB: How to plot phase portrait given a system of equations

differential equationode45phase portraits

Suppose I have the system represented as
How would I plot the phase portriats for A=0.5,1, and 3? I know how to do it if I was given the equations, but I am confused how I would do it given matrix notation. Thank you.

Best Answer

Do you mean something like this
A = 0.5;
M = [A 0; 1 A];
dXdt = @(t,X) M*X;
tspan = [0 1];
X0 = [1; 1];
[t, X] = ode45(dXdt, tspan, X0);
x1 = X(:,1); x2 = X(:,2);
V = dXdt(t,X')';
v1 = V(:,1); v2 = V(:,2);
figure
plot(t,x1,t,x2), grid
xlabel('t'),ylabel('x')
legend('x1','x2')
figure
subplot(2,1,1)
plot(x1,v1),grid
xlabel('x1'),ylabel('v1')
subplot(2,1,2)
plot(x2,v2),grid
xlabel('x2'),ylabel('v2')
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