For citation:
Kruglov V. P. Attractor of smale–williams type in a ring system with periodic frequency modulation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 1, pp. 124-128. DOI: 10.18500/0869-6632-2012-20-1-124-128
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Russian
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UDC:
517.9
Attractor of smale–williams type in a ring system with periodic frequency modulation
Autors:
Kruglov Vjacheslav Pavlovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract:
A scheme of circular nonautonomous system is introduced, which is supposed to generate hyperbolic chaos. Its operation is based on doubling of phase on complete cycle of the signal transmission. This is a criterion for the Smale–Williams attractor to exist. The performance is realized due to smooth periodic variation of natural frequency in one of the two oscillatory subsystems, which compose the ring, from reference value to the doubled one.
Reference:
- Kuznetsov SP. Hyperbolic Chaos: A Physicist’s View. Higher Education Press: Beijing and Springer-Verlag, Berlin, Heidelberg; 2012. 336 p.
- Kuznetsov SP. Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics. Phys. Usp. 2011;54(2):119–144. DOI: 10.3367/UFNe.0181.201102a.0121.
- Kuznetsov SP. Example of a physical system with a hyperbolic attractor of the Smale–Williams type. Phys. Rev. Lett. 2005;95:144101. DOI: 10.1103/PhysRevLett.95.144101.
- Kuznetsov AP, Kuznetsov SP, Pikovsky AS, Turukina LV. Chaotic dynamics in the systems of coupling nonautonomous oscillators with resonance and nonresonance communicator of the signal. Izvestiya VUZ. Applied Nonlinear Dynamics. 2007;15(6):75–85 (in Russian). DOI: 10.18500/0869-6632-2007-15-6-75-85.
- Kuznetsov SP. Dynamic chaos. Moscow: Fizmatlit; 2006. 356 p. (in Russian).
Received:
13.02.2012
Accepted:
13.02.2012
Published:
20.04.2012
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