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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 1, Pages 53–59
(Mi nd55)
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Invariant tori and chaotic dynamics in a nonlinear nonautonomous Reyleigh-like equation
L. A. Belyakovab, G. V. Belyakovaab a Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
b N. I. Lobachevski State University of Nizhni Novgorod, Faculty of Computational Mathematics and Cybernetics
Abstract:
For a nonlinear Reyleigh-like system with a periodic perturbation, we give some fragments of the study to be connected with the problems of the existence of both chaotic dynamics and invariant tori of certain types. We construct bifurcation diagrams explaining a character of boundaries for regions corresponding to the existence of chaotic dynamics and the invariant tori. Besides, we construct bifurcation curves (for a series of periodic motions) which play the principal role at scenarios of creation of the boundaries pointed out.
Keywords:
dynamical chaos, closed invariant curve, bifurcation set, homoclinic tangency, resonance.
Received: 17.03.2010
Citation:
L. A. Belyakov, G. V. Belyakova, “Invariant tori and chaotic dynamics in a nonlinear nonautonomous Reyleigh-like equation”, Nelin. Dinam., 6:1 (2010), 53–59
Linking options:
https://www.mathnet.ru/eng/nd55 https://www.mathnet.ru/eng/nd/v6/i1/p53
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