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JOURNALS // Izvestiya VUZ. Applied Nonlinear Dynamics // Archive

Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, Volume 22, Issue 1, Pages 27–54 (Mi ivp219)

APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY

Synchronization and multi-frequency quasi-periodicity in the dynamics of coupled oscillators

A. P. Kuznetsovab, L. V. Turukinaab, I. R. Sataeva, N. Yu. Chernyshovb

a Saratov Branch, Kotel'nikov Institute of Radio-Engineering and Electronics, Russian Academy of Sciences
b Saratov State University

Abstract: The dynamics of ensembles of oscillators containing a small number of bibitemlits is discussed. The possible types of regimes and pecularities of bifurcations of regular and quasi-periodic attractors are analyzed. By using the method of Lyapunov exponents charts the picture of embedding of quasi-periodic regimes of different dimension in the parameter space is revealed. Dynamics of ensembles of van der Pol and phase oscillators are compared.

Keywords: Synchronization, quasi-periodic oscillations, invariant tori, bifurcation.

UDC: 517.9

Received: 19.12.2013



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