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Nelin. Dinam., 2014, Volume 10, Number 4, Pages 387–405 (Mi nd452)  

Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity

Alexander P. Kuznetsovab, Natalia A. Migunovaa, Igor R. Sataevb, Julia V. Sedovab, Ludmila V. Turukinaab

a Saratov State University, Astrahanskaya 83, Saratov, 410012, Russia
b Kotelnikovs Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelenaya 38, Saratov, 410019, Russia

Abstract: Ensembles of several chaotic Rössler oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of invariant tori of different and sufficiently high dimension. The possibility of a quasi-periodic Hopf bifurcation and of the cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonant tori are revealed whose boundaries correspond to a saddle-node bifurcation. Within areas of resonant modes the torus-doubling bifurcations and tori destruction are observed.

Keywords: chaos, quasiperiodic oscillations, invariant tori, Lyapunov exponents, bifurcations.

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UDC: 537.86
MSC: 70K43, 65P20, 65P30, 34D08
Received: 10.09.2014
Revised: 10.10.2014

Citation: Alexander P. Kuznetsov, Natalia A. Migunova, Igor R. Sataev, Julia V. Sedova, Ludmila V. Turukina, “Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity”, Nelin. Dinam., 10:4 (2014), 387–405

Citation in format AMSBIB
\Bibitem{KuzMigSat14}
\by Alexander~P.~Kuznetsov, Natalia~A.~Migunova, Igor~R.~Sataev, Julia~V.~Sedova, Ludmila~V.~Turukina
\paper Dynamics of coupled chaotic oscillators: from chaos to quasiperiodicity
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 4
\pages 387--405
\mathnet{http://mi.mathnet.ru/nd452}


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