phase difference of oscillators

How do I take the phase difference of oscillators across time

Answer 1

[Star Strider]

It depends on whether the phase relationship is constant or changes, and what the data are. If it is constant, calculating them is relatively straightforward using Product-to-sum and sum-to-product identities, and other relationships.

[Samson]

Thanks for your answer. The phase relationship changes. I had use this below calculating the phase velocity over time across the last 2500 samples and taking the mean. However, I discovered I was actually calculting across oscillators and not time. So I need help in calculating, using the correct codes

phdiff=diff(X');

temp=phdiff./dt;

phvel=temp(:,end-2500:end);

omegav=mean(phvel);

omega=max(omegav)-min(omegav);

[Star Strider]

It would appear that if the phase difference changes over time, it would be necessary to calculate across oscillators and across time.

Again, I have no idea what the data are.

One option could be to use findpeaks to see the differences in the peak times over time. Another related approach would be to get the approximate zero-crossing indices of each signal using:

zxi = @(s) find(diff(sign(s)));

then interpolste in the region of each zero-crossing to get the most precise estimates possible of the zero-crossing times. It might be necessary to use a highpass (or bandpass) filter to remove any baseline variations and constant offsets (and possibly high-frequency noise) first.

[Samson]

My data is generated from a nonlinear ordinary differential equation integrated with random initial conditions over time with time step of 0.05 (dimensionless)

[Star Strider]

I cannot go any farther without bveing able to simulate them.

[Samson]

I really appreciate your help. I have already integrated the system and got a solution say X. This X is a matrix of 50 X 20000 samples. I need to now do d(X)/dt and take the mean say for the last 2500 samples. I hope you understand

[Star Strider]

My pleasure!

I am not certain that I do understand.

However not knowing anything at all about the details of your system, note that you can use the gradient function to get the derivatives, specifically:

dXdt = gradient(X) ./ gradient(t);

With a matrix, that calculation could be less than obvious. See the documentation for the gradient function for details of what to use as outputs and how to specify the result.

[Samson]

Thank you so much for your time. I deeply appreciate it. How I wish I could show you my entire code!

[Star Strider]

My pleasure!

You could of course Accept my Answer!

I did the best I could, considering the imposed constraints.

[Samson]

Please note that the data ia a time series data in which I have integrated and gotten a solntion say X. What I needed is to find the mean phase velocity of X