How to implement coupled ordinary differential equations in Matlab

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

[Azzi Abdelmalek]

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]);

[Aniket]

Hello Azzi,

Thank you for your answer and still small doubt that....i want to implement adaptive hopf oscillator so that oscillator frequency(w) learn the perturbation signal (F) frequency ...so that they have given the learning rule for this learning rule for this adaptation is

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

so how should i implement this state variable with above code?

thank you.

Answer 2

[Teratora]

Hi,

It's been a long time since this was posted and I was wondering if you had finally made it work Aniket, as I am trying to do exactly that right now. I'm going to try coupling several adaptive Hopf oscillators, but need to start with the beginning, right? ;-)

Hope you'll answer! Thanks =)

[Hartvik Line]

I found some MATLAB example files for Hopf bifurcation that might help you get started

http://www.isnld.com/indexC.html

[Shritej Chavan]

Hi Teratora,

It's been a long time since you asked this question and I was wondering if you really implemented network coupled adaptive Hopf oscillators. I am trying to do exactly that right now. I am copying your words but I am serious. I am struggling and I need help.

Hope you will answer! Thanks in advance .