How do you add white noise to a nonlinear ODE?

I have the following system of differential equations and am trying to add GWN to the input.

f = @(t,y) [alpha * (y(2) + y(1) - (y(1).^3)/3 + ( k1 + c * y(3)+ x));

    (-1/alpha) * (w2 * y(1) - a + b * y(2));

    alpha * (y(4) + y(3) -( y(3).^3)/3 + (k2 + c * y(1))); 

    (-1/alpha) * (w2 * y(3) - a + b * y(4)) ];

[T Y] = ode15s(f, [0 1000], [0, 0, 0, 0]);

The input is in bold and the noise is represented by the x. The noise is bandlimited and was created as follows:

% Generate Gaussian White Noise

gwn = wgn(N,1,20);

% create butterworth filter

Wn = 5/(fs/2); %cutoff frequency

[b, a] = butter(4,Wn, 'low'); % get filter coefficients

w = filter(b,a,gwn); % apply filter

However, when I try to add this to my ode, I get the following error:

Error in ==> odearguments at 98 f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ==> ode15s at 227 [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in ==> Main_ImR at 29 [T Y] = ode15s(f, [0 1000], [0, 0, 0, 0]);

In this case,

a = 0.7; b = 0.8; w2 = 1; alpha = 3; k1 = -1; k2 = -1; c = 0.5;

Why am I getting this error and how would I go about adding the noise to the ode?

Answer 1

[Torsten]

x must be a scalar in your ODE function - I doubt that this is the case.

Best wishes

Torsten.

[EL890]

it is not, unfortunately. It is also time dependent.

[Torsten]

Define f in a function, not as a function handle. Then you can interpolate x to the time t where it is required by the solver.

Take a look at the paragraph "ODE with time-dependent terms" under

https://de.mathworks.com/help/matlab/ref/ode45.html

for an example.

Best wishes

Torsten.

[EL890]

great, thanks Torsten