How to implement network of 'n' coupled adaptive Hopf oscillators ?

I am trying to implement network of adaptive coupled Hopf oscillators which is able to learn any periodic input signal (F(t)).

Each oscillator is given by 5 state variables, 2 oscillatory motion that assure structural stability ( xi, yi), one for learning the frequency (wi), one for amplitude (ai) and one for phase relations (oi).

The network summarizes in the following equations, where i represent the oscillator is the (except for oscillator 0):

whereas for oscillator 0 only first four equations are considered with 'tau*sin(Ri - oi) = 0'.

My code for oscillator 0 is as follows:

function dz = myeqd(t,x,fi,ti, epsilon, mu, gamma, eta) 

%gamma - speed  of convergence

%mu - radius of limit cycle 

%epsilon & eta - coupling constant

F_t = interp1(ti,fi, t);

k = gamma*(mu - (x(1)^2 + x(2)^2))*x(1) - x(3)*x(2) + epsilon*(F_t) ;

y = gamma*(mu - (x(1)^2 + x(2)^2))*x(2) + x(3)*x(1) ;

w = -epsilon*(F_t)*x(2)/(x(1)^2 + x(2)^2) ; 

a = eta*x(1)*(F_t);

dz = [k;y;w;a] ; 

end

In the command window

ti = 0:0.1:2000 ;

t = ti ;

fi = sin(40*t) ;

[t,x] = ode45(@(t,x)myeqd(t,x,fi,ti,0.9, 1,17, 0.9), t , [1 0 45 1] ) ;

*The problem is the amplitude does not converge to a proper value but the frequency does and the amplitude keeps increasing after time when the oscillator has learned the correct frequency.

Also I want expand this code for n oscillators represented by the above equations by proper coupling between oscillators to ensure phase relations.

[Praveen Kumar Pakkiri Samy]

I have implemented a similar adaptive oscillator using matlab and simulink. It can be found here:

https://github.com/Prajonty/Adaptive-Oscillators

Good luck!!

Answer 1

[Hmayag Partamian]

Hello Shritej,

I have been recently trying to implement the same application as well and I have stumbled into the same problem where the Amplitude keeps on increasing.

Have you managed to find a solution to the problem?

I appreciate your help in case you solved the issue.

nb. in your code sqrt was missing.

w = -epsilon*(F_t)*x(2)/sqrt(x(1)^2 + x(2)^2) ;

Regards,

Hmayag Partamian

[Praveen Kumar Pakkiri Samy]

you can check this

https://github.com/Prajonty/Adaptive-Oscillators

[Hmayag Partamian]

Thank you Praveen.

Is there an article we can refer too just in case (mathematical formulations, experiements, citing for code if used,..) ?

Thanks again

Answer 2

[tangjia zhang]

Hi，Shritej

there are two problem for your code，（1）the time step you should get smaller，like 0.001，(2)the input should be F=F_t-x(1),use this one to replace your F_t in your code.