Dear KL,

I think that it is important to give a precise description of the physical model of the system of oscillators and accordingly based on the physical model you can develop the mathematical model with independent and dependent performance functional parameters. Then you can investigate how do you determine the model independent parameters which means: which measurements you need to get the system unknowns from observing its performance parameters.

Best wishes

Dear KL,

I think that it is important to give a precise description of the physical model of the system of oscillators and accordingly based on the physical model you can develop the mathematical model with independent and dependent performance functional parameters. Then you can investigate how do you determine the model independent parameters which means: which measurements you need to get the system unknowns from observing its performance parameters.

Best wishes

Dear KL,

For solving of your problem I would use Takens theorem, Empirical Mode Decomposition and Hilbert-Huang Transform. I think that using this tools and some priory information about system I would manage with problem.

Best wishes

Thank you all for the replies!!! Andreas Otto and Alex Ru, can you share share some references that you are aware of?

Andreas Otto

wrt points 1 and 4) if I choose to look at the raw data and not use Hilbert Transformation, what aspects of the signal during transients are you referring to when you say they are more informative?

2) I am completely new to Takens and so the question might sound dumb but, suppose I have models which describe the individual oscillators of my system and a few potential coupling functions (non experimentally validated though), can I still use Takens embedding to extract any information from the time series of the entire network?

5) There is most likely to be a time delay and I understand the principle behind your point but can you please share some references on this topic for my reading?

Thanks once again!

Dear KL,

By revisiting you question, i read the question again and i would like to make a proposal for you. If you can acquire the integrated or the combined dynamic output of all the oscillators, then you can use the Fourier transform to get the the oscillation frequencies. By analyzing them you can get the possible coupling between the oscillators.If the oscillators are weakly coupled then then one sees the discrete self oscillating frequency. If the coupling is high it will lead to shift in the oscillation frequencies to give sum and differences in frequencies. This is a known fact from the coupled resonators. The important thing that the acquired waveform length must be sufficiently long to contain the lowest possible frequency.

On the other side is that the sampling frequency must be high enough to resolve the highest possible frequency.

Best wishes

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Sysoev I. V., Ponomarenko V. I., Pikovsky A. Reconstruction of coupling architecture of neural field networks from vector time series // Commun. Nonlinear Sci. Numer. Simulat. — 2018. — Vol. 57. — Pp. 342–351. — DOI: 10.1016/j.cnsns.2017.10.006.