This article is cited in 1 scientific paper (total in 1 paper)
Reconstruction of the coupling matrix in the ensemble of identical neuron-like oscillators with time delay in coupling
I. V. Sysoeva, V. I. Ponomarenkoab
a National Research Saratov State University,
ul. Astrakhanskaya 83, Saratov, 410012, Russia
b Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch,
ul. Zelenaya 38, Saratov, 410019, Russia
Reconstruction of equations of oscillatory systems from time series is an important problem, since results can be useful in different practical applications, including forecast of future dynamics, indirect measurement of parameters and diagnostics of coupling. The problem of reconstruction of coupling coefficients from time series of ensembles of a large number of oscillators is a practically valid problem. This study aims to develop a method of reconstruction of equations of an ensemble of identical neuron-like oscillators in the presence of time delays in couplings based on a given general form of equations.
The proposed method is based on the previously developed approach for reconstruction of diffusively coupled ensembles of time-delayed oscillators. To determine coupling coefficients, the target function is minimized with least-squares routine for each oscillator independently. This function characterizes the continuity of experimental data. Time delays are revealed using a special version of the gradient descent method adapted to the discrete case.
It is shown in the numerical experiment that the proposed method allows one to accurately estimate most of time delays ($\sim$ 99%) even if short time series are used. The method is asymptotically unbiased.
time series, ensembles of oscillators, time delay in coupling, reconstruction of equations
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I. V. Sysoev, V. I. Ponomarenko, “Reconstruction of the coupling matrix in the ensemble of identical neuron-like oscillators with time delay in coupling”, Nelin. Dinam., 12:4 (2016), 567–576
Citation in format AMSBIB
\by I.~V.~Sysoev, V.~I.~Ponomarenko
\paper Reconstruction of the coupling matrix in the ensemble of identical neuron-like oscillators with time delay in coupling
\jour Nelin. Dinam.
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This publication is cited in the following articles:
I. V. Sysoev, V. I. Ponomarenko, M. D. Prokhorov, “Reconstruction of ensembles of oscillators with nonlinear time-delay feedbacks”, Tech. Phys. Lett., 44:11 (2018), 1024–1027
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