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Nelin. Dinam., 2012, Volume 8, Number 5, Pages 863–873 (Mi nd375)  

This article is cited in 2 scientific papers (total in 2 papers)

Landau–Hopf scenario in the ensemble of interacting oscillators

Alexander P. Kuznetsov, Sergey P. Kuznetsov, Ludmila V. Turukina, I. R. Sataev

Saratov Branch of Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov, Russia

Abstract: The conditions are discussed for which the ensemble of interacting oscillators may demonstrate Landau–Hopf scenario of successive birth of multi-frequency regimes. A model is proposed in the form of a network of five globally coupled oscillators, characterized by varying degree of excitement of individual oscillators. Illustrations are given for the birth of the tori of increasing dimension by successive quasi-periodic Hopf bifurcation.

Keywords: synchronization, bifurcations, quasi-periodic dynamics, chaos.

Full text: PDF file (578 kB)
References: PDF file   HTML file
UDC: 517.9
MSC: 39Axx, 93D05
Received: 24.09.2012
Revised: 19.10.2012

Citation: Alexander P. Kuznetsov, Sergey P. Kuznetsov, Ludmila V. Turukina, I. R. Sataev, “Landau–Hopf scenario in the ensemble of interacting oscillators”, Nelin. Dinam., 8:5 (2012), 863–873

Citation in format AMSBIB
\Bibitem{KuzKuzTur12}
\by Alexander~P.~Kuznetsov, Sergey~P.~Kuznetsov, Ludmila~V.~Turukina, I.~R.~Sataev
\paper Landau--Hopf scenario in the ensemble of interacting oscillators
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 5
\pages 863--873
\mathnet{http://mi.mathnet.ru/nd375}


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    This publication is cited in the following articles:
    1. A. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, N. Yu. Chernyshov, “Sinkhronizatsiya i mnogochastotnaya kvaziperiodichnost v dinamike svyazannykh ostsillyatorov”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 22:1 (2014), 27–54  zmath  elib
    2. A. P. Kuznetsov, S. P. Kuznetsov, Yu. V. Sedova, “Mayatnikovaya sistema s beskonechnym chislom sostoyanii ravnovesiya i kvaziperiodicheskoi dinamikoi”, Nelineinaya dinam., 12:2 (2016), 223–234  mathnet  elib
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