MATLAB: Nonlinear ordinary differntial equations

ode

i have three nonlinear oscillator equation

1 ) dx/dt = (mu-x^2-y^2)x – w*y +K*F

2) dy/dt = (mu-x^2-y^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)

dw/dt is learning rule for intrinsic frequency (as it learn frequency of input signal F)

x and y are state variables

how could i implement it in MATLAB ?

Start with ODE45, take a look at this example and it will help you get started:

The third equation will be

dz(3) = (-K*F)*y(2)/sqrt(y(1)^2+y(2)^2)

with

dz = zeros(3,1);

By integrating both sides of the equation:

integral_{y=y0}^{y=y}y*(a-y) dy = (a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3)
integral_{x=x0}^{x=x}u/k dx = u/k*(x-x0)

Thus

(a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3) = u/k*(x-x0)

and the inverse function if the solution is given by

x = x0 + k/u*((a*y^2/2 - y^3/3) - (a*y0^2/2 - y0^3/3))

Best wishes

Torsten.