RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Nelin. Dinam.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Nelin. Dinam., 2016, Volume 12, Number 4, Pages 567–576 (Mi nd538)  

This article is cited in 1 scientific paper (total in 1 paper)

Original papers

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 Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russia

Abstract: 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.

Keywords: time series, ensembles of oscillators, time delay in coupling, reconstruction of equations

Funding Agency Grant Number
Russian Foundation for Basic Research 16-34-00203
16-02-00091
Ministry of Education and Science of the Russian Federation -1510.2015.4


DOI: https://doi.org/10.20537/nd1604002

Full text: PDF file (335 kB)
References: PDF file   HTML file

UDC: 530.182, 51-73
MSC: 37M10
Received: 21.09.2016
Accepted:14.10.2016

Citation: 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
\Bibitem{SysPon16}
\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.
\yr 2016
\vol 12
\issue 4
\pages 567--576
\mathnet{http://mi.mathnet.ru/nd538}
\crossref{https://doi.org/10.20537/nd1604002}
\elib{http://elibrary.ru/item.asp?id=27715763}


Linking options:
  • http://mi.mathnet.ru/eng/nd538
  • http://mi.mathnet.ru/eng/nd/v12/i4/p567

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  crossref  isi  scopus
  • Number of views:
    This page:99
    Full text:37
    References:14

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020