## How to implement coupled ordinary differential equations in Matlab

### Aniket (view profile)

on 13 Jan 2013
Latest activity Commented on by Shritej Chavan

on 19 May 2018

### Azzi Abdelmalek (view profile)

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))]

### Azzi Abdelmalek (view profile)

on 13 Jan 2013
Edited by Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 13 Jan 2013

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
t=ti;
[t,y]=ode45(@(t,y) dif_eq(t,y,ti,fi),t,[0;0]);

Aniket

### Aniket (view profile)

on 13 Jan 2013
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.

### Teratora (view profile)

on 11 Mar 2015

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? ;-)

Hartvik Line

### Hartvik Line (view profile)

on 7 Feb 2018
I found some MATLAB example files for Hopf bifurcation that might help you get started
Shritej Chavan

### Shritej Chavan (view profile)

on 19 May 2018
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.