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

For citation:

Arzhanukhina D. S., Kuznetsov S. P. System of three nonautonomous oscillators with hyperbolic chaos. Part I The model with dynamics on attractor governed by Arnold’s cat map on torus. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 6, pp. 56-66. DOI: 10.18500/0869-6632-2012-20-6-56-66

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2012-20-6-56-66

System of three nonautonomous oscillators with hyperbolic chaos. Part I The model with dynamics on attractor governed by Arnold’s cat map on torus

Autors: 
Arzhanukhina Darja Sergeevna, Saratov State University
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

In this paper a system of three coupled nonautonomous self-oscillatory elements is studied, in which the behavior of oscillators phases on a period of the coefficients variation in the equations corresponds to the Anosov map demonstrating chaotic dynamics. Results of numerical studies allow us to conclude that the attractor of the Poincare map can be viewed as an object roughly represented by a two-dimensional torus embedded in the sixdimensional phase space of the Poincare map, on which the dynamics is the hyperbolic ´ chaos intrinsic to Anosov’s systems.

Key words: 
Attractor
hyperbolic chaos
Anosov map
Arnold’s cat map
Fibonacci map
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Received: 
22.06.2012
Accepted: 
04.09.2012
Published: 
29.03.2013
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