MATLAB: How to implement coupled ordinary differential equations in Matlab

Question

I am trying to implement adaptive hopf oscillator.

i have to implement these dynamics eqution

dx/dt = (mu – r^2)x – wy +KF(t)

dy/dt = (mu – r^2)y + wx

where , mu = 1 and initial condition of r(0)= 1 (r = root(x^2 + y^2))

F(t) is time periodic perturbation means any input signal and K is coupling strength , w is intrinsic frequency of oscillator

learning rule for this adaptation is

dw/dt = -KF(t) * [y/(root (x^2+y^2))]

Answer 1

function dz=myeqd(t,y,ti,fi)
mu=0.7;
r=1;
K=1;
w=1;
F=interp1(ti,fi,t);
dz(1)= (mu - r^2)*y(1) - w*y(2) +K*F;
dz(2) = (mu - r^2)*y(2) + w*y(1);

Then call the above function

ti=[0.1:0.1:10]; % time vector
fi=rand(1,numel(t)); % your perturbation
t=ti;
[t,y]=ode45(@(t,y) dif_eq(t,y,ti,fi),t,[0;0]);