Reconstruction of the coupling matrix in the ensemble of identical neuron-like oscillators with time delay in coupling

I. V. Sysoev ; V. I. Ponomarenko

Russian journal of nonlinear dynamics, Tome 12 (2016) no. 4, pp. 567-576

Résumé

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.

Détail

Keywords: time series, time delay in coupling
Mots-clés : ensembles of oscillators, reconstruction of equations.