ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Kuznetsov A. P., Turukina L. V. «Oscillator death» and quasiperiodic bifurcations in low-dimensional ensemble of van der Pol oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics, 2013, vol. 21, iss. 2, pp. 135-144. DOI: 10.18500/0869-6632-2013-21-2-135-144

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Language: 
Russian
Heading: 
Bifurcations in Dynamical Systems
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2013-21-2-135-144

«Oscillator death» and quasiperiodic bifurcations in low-dimensional ensemble of van der Pol oscillators

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Turukina L. V., Saratov State University
Abstract: 

The dynamics of the four dissipatively coupled van der Pol oscillator is considered. Lyapunov chart is presented in the parameter plane and its arrangement is discusses. The effect of increase of the threshold for the «oscillator death» regime and the possibility of complete and partial broadband synchronization are revealed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators, in particular, quasiperiodic saddle-node and Hopf bifurcations.

Key words: 
synchronization
oscillator death
quasi-periodic bifurcations
Reference: 
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Received: 
21.09.2012
Accepted: 
19.12.2012
Published: 
31.07.2013
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