How to represent a chaotic trajectory in MatLab?

Hello everyone. I tried to represent the following ODE system in Matlab but I don't know how to find if it has chaotic trajectory or not. Any ideas?

ODEfcn = @(t,x,a) [0.25*(a*x(1)*(1-x(1))) - 0.0015*x(2) - 0.3*x(1); 0.25*x(1)*(1-x(1)) - 0.0515*x(2)];
ic = [1 1];
tspan = [0 50];
a = 2;                                                     
[t,y] = ode45(@(t,x)ODEfcn(t,x,a), tspan, ic);
figure
plot(t, y)
grid

Answer 1

[Star Strider]

I remember this system. I do not know what you intend by ‘chaotic trajectory’ here.

If you want to plot the derivative of ‘k’ with respect to time as a function of the derivatve of ‘y’ with respect to time, this works:

for k = 1:numel(t)
    ddt(k,:) = ODEfcn(t(k),y(k,:),a);                       % Calculate Derivatives From Solved Values & ‘ODEfcn’
end

figure
plot(ddt(:,1), ddt(:,2))
grid
axis equal
xlabel('$\frac{dy(t)}{dt}$', 'Interpreter','latex')
ylabel('$\frac{dk(t)}{dt}$', 'Interpreter','latex')

The integrated functions themselves are given by ‘y(:,1)’ for ‘y’, and ‘y(:,2)’ for ‘k’ (remembering those from your earlier Question).