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


For citation:

Kuznetsov A. P., Kuznetsov S. P., Pikovsky A. S., Turukina L. V. Chaotic dynamics in the systems of coupling nonautonomous oscillators with resonance and nonresonance communicator of the signal. Izvestiya VUZ. Applied Nonlinear Dynamics, 2007, vol. 15, iss. 6, pp. 75-85. DOI: 10.18500/0869-6632-2007-15-6-75-85

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Language: 
Russian
Article type: 
Article
UDC: 
517.9

Chaotic dynamics in the systems of coupling nonautonomous oscillators with resonance and nonresonance communicator of the signal

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

Chaotic dynamics in the systems of coupling nonautonomous van der Pol oscillators with resonance and nonresonance communicator of the signal is considered. For the both models phase map for the period of the external force are show hyperbolic attractor of the Smale–Williams type. In these models features of chaotic dynamics investigated depending on type of the communicator of the signal.

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Reference: 
  1. Sinai YaG. Stochasticity of Dynamic Systems. In: Gaponov AV. Nonlinear Waves. Moscow: Nauka; 1979. (in Russian).
  2. Guckenheimer J, Holmes P. Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Moscow-Izhevsk: Institute of Computer Research; 2002. 559 p. (in Russian).
  3. Devaney RL. An Introduction to Chaotic Dynamical Systems. NY: Addison-Wesley; 1989.
  4. Shilnikov L. Mathematical problems of nonlinear dynamics: a tutorial. Int. J. of Bif. and Chaos. 1997;7(9):1953–2001. DOI: 10.1142/S0218127497001527.
  5. Katok A, Hasselblatt B. Introduction to the Modern Theory of Dynamical Systems. Trans. from English. Moscow: Factorial; 1999. (in Russian).
  6. Afraimovich V, Hsu SB. Lectures on chaotic dynamical systems. AMS/IP Studies in Advanced Mathematics, Vol.28. American Mathematical Society, Providence RI, International Press, Somerville, MA; 2003.
  7. Ott E. Chaos in Dynamical Systems. Cambridge: Cambridge University Press; 1993.
  8. Anishchenko VS, Astakhov VV, Vadivasova TE, Neiman AB, Strelkova GI, Schimansky-Geier L. Nonlinear Effects in Chaotic and Stochastic Systems. Izhevsk: Institute of Computer Sciences; 2003.
  9. Kuznetsov SP. Example of a physical system with a hyperbolic attractor of a Smale–Williams type. Phys. Rev. Lett. 2005;95:144101. DOI: 10.1103/PhysRevLett.95.144101.
  10. Belykh V, Belykh I, Mosekilde E. Hyperbolic Plykin attractor can exist in neuron models. Int. J. of Bif. and Chaos. 2005;15(11):3567–3578. DOI: 10.1142/S0218127405014222.
  11. Kuznetsov SP, Seleznev EP. A strange attractor of the Smale-Williams type in the chaotic dynamics of a physical system. Journal of Experimental and Theoretical Physics. 2006;102(2):355–364. DOI: 10.1134/S1063776106020166.
  12. Kuznetsov AP, Sataev IR. Verification of hyperbolicity conditions for a chaotic attractor in a system of coupled nonautonomous van der Pol oscillators. Izvestiya VUZ. Applied Nonlinear Dynamics. 2006;14(5):3–29 (in Russian). DOI: 10.18500/0869-6632-2006-14-5-3-29.
  13. Kuznetsov SP. Dynamic chaos. 2nd ed. Moscow: Fizmatlit; 2006. 356 p. (in Russian).
Received: 
26.06.2007
Accepted: 
26.06.2007
Published: 
30.01.2008
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