i have three nonlinear oscillator equation
1 ) dx/dt = (mu-r^2)x – w*y +K*F
2) dy/dt = (mu-r^2)y + w*x
3) dw/dt = (-K*F)*(y/(sqrt(x^2+y^2)))
here,
F is any input signal
K is coupling strength (K > 0 is any value)
w is oscillator intrinsic frequency
mu is constant (mu > 0 any value)
r is taking as a constant here .. r=1
third equation dw/dt is learning rule for intrinsic frequency (as w learn frequency of input signal F) and i am getting stuck in this part of equation that how could i implement this part and integrate it in matlab code ?
x and y are state variables.
the following is matlab code without third equation and i want to integrate third equation in this code.
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function dz = myeqd(t,y,ti,fi)
dz = zeros(2,1);
mu=0.7;
r=1;
K=1;
w=40;
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);
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calling this myeqd function
Tspan= [0.1:0.1:10]; % time vector
t= Tspan;
fi = cos(2*pi*Tspan); % perturbation
ti=Tspan;
[T,Y]=ode45(@(t,y) myeqd(t,y,ti,fi),Tspan,[0;1]);
plot (T,Y)
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