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

For citation:

Kuznetsov A. P., Sataev I. R., Sedova Y. V., Turukina L. V. On modelling the dynamics of coupled self-oscillators using the simplest phase maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 2, pp. 112-137. DOI: 10.18500/0869-6632-2012-20-2-112-137

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Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Other
UDC: 
517.9
DOI: 
10.18500/0869-6632-2012-20-2-112-137

On modelling the dynamics of coupled self-oscillators using the simplest phase maps

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

The problem of describing the dynamics of coupled self-oscillators using discrete time systems on the torus is considered. We discuss the methodology for constructing such maps as a simple formal models, as well as physically motivated systems. We discuss the differences between the cases of the dissipative and inertial coupling. Using the method of Lyapunov exponents charts we identify the areas of two- and three-frequency quasiperiodicity and chaos. Arrangement of the Arnold resonance web is investigated and compared for different model systems. 

Key words: 
synchronization
quasi-periodical oscillations
phase maps
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Received: 
31.01.2012
Accepted: 
05.03.2012
Published: 
29.06.2012
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