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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 5, Pages 737–743 (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

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.

DOI: https://doi.org/10.7868/S0044466913050074

Full text: PDF file (428 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:5, 573–579

Bibliographic databases:

UDC: 519.62
Received: 18.11.2011
Revised: 09.12.2012

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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    This publication is cited in the following articles:
    1. L.-N. Zhang, F.-Ch. Li, X. Yu, P.-F. Cui, X.-Y. Wang, “Experimental research on 2:1 parametric vibration of stay cable model under support excitation”, Adv. Mater. Sci. Eng., 2016, 9804159  crossref  isi  scopus
    2. L.-N. Zhang, F.-Ch. Li, X.-Y. Wang, P.-F. Cui, “Theoretical and numerical analysis of 1:1 main parametric resonance of stayed cable considering cable-beam coupling”, Adv. Mater. Sci. Eng., 2017, 6948081  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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