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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 5, Pages 737–743
DOI: https://doi.org/10.7868/S0044466913050074 (Mi zvmmf9854) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance

A. Yu. Koverga, E. P. Kubyshkin

P. G. Demidov Yaroslavl State University
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DOI: https://doi.org/10.7868/S0044466913050074
Abstract: Two-frequency parametric resonance in nonlinear dynamical systems is studied by analyzing a delay differential equation with the delay obeying a two-frequency law, which arises in the mathematical simulation of some physical processes. It is shown that the system can exhibit chaotic oscillations (strange attractors) when the parametric excitation frequencies are both close to the doubled eigenfrequency of the system (degenerate case). The formation mechanisms of chaotic attractors are discussed, and the Lyapunov exponents and the Lyapunov dimension are calculated for them. If only one of the parametric excitation frequencies is close to the double eigenfrequency, a two-frequency regime occurs in the system.
Key words: delay differential equations, parametric resonance in nonlinear dynamical systems, chaotic oscillations, strange attractor.
Received: 18.11.2011
Revised: 09.12.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 5, Pages 573–579
DOI: https://doi.org/10.1134/S0965542513050060
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: A. Yu. Koverga, E. P. Kubyshkin, “Features of the behavior of solutions to a nonlinear dynamical system in the case of two-frequency parametric resonance”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 737–743; Comput. Math. Math. Phys., 53:5 (2013), 573–579
Citation in format AMSBIB
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