Finding Angular Frequency of an Oscillation

I have currently produced a code to plot a Van der Pol oscillator, I can calculate the period by physically looking at the graph, but I am unsure on how to do this using a MATLAB code to get a result digitally.

My main focus is to get a printed value for the angular frequency (w - omega), so my first thought was to calculate the period and then use the equation w = (2pi/T).

Please can I get some guidance on producing a small script to calculate angular frequency? (w = 1 with the current model)

I have attached the code for the oscillation below.

Thanks in advance.

% simulation parameters
DT = 0.01;                   % Time step
N  = 10000;                 % number of discrete time points

% Equation parameter
mu = 0.1;

% declare array to store discrete time samples
x = zeros(1,N);

% set boundary conditions
x(1) = -0.01;
x(2) =  0.0;

% Simulate using recurrance relation
for i = 3:N   
    phi = mu*DT/2*(x(i-1)^2-1);
    x(i) = x(i-1)*(2-DT^2)/(1+phi) - x(i-2)*(1-phi)/(1+phi);
end

% plot
plot((1:N)*DT,x,'r')

% Calculating angular frequency

Answer 1

[Star Strider]

Likely the easiest way would be to find the times of the positive peaks, then calculate from there:

[pks,pktimes] = findpeaks(x, (1:N)*DT);
Period = mean(diff(pktimes))

The findpeaks function requires the Signal Processing Toolbox. A similar function is islocalmax, introduced in R2017b. (There are still other ways if you have neither of these functions.)

[Macaulay Wright]

Thank you for the quick response, that piece of code works perfectly and was just what I was trying to acheive. I will now input the angular frequency equation using the new found period value.

Thank you again.

[Star Strider]

As always, my pleasure!