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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2011, Volume 7, Number 3, Pages 437–449
(Mi nd269)
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This article is cited in 1 scientific paper (total in 1 paper)
On global behaviour of the solutions of system of two Duffing – Van der Pole equations
R. E. Kondrashov, A. D. Morozov N. I. Lobachevski State University of Nizhni Novgorod, Prospekt Gagarina 23, Nizhni Novgorod, 603950, Russia
Abstract:
The problem of global behavior of solutions in system of two Duffing – Van der Pole equations close to nonlinear integrable is considered. For regions without unperturbed separatrixes we give partially averaged systems which describe the behavior of solutions of original system in resonant zones. The finiteness of number of non-trivial resonant structures is established. Also we give fully averaged systems which describe the behavior of solutions outside of neighborhoods of nontrivial resonant structures. The results of numerically investigation of these systems are resulted.
Keywords:
limit cycles, resonances, averaging.
Received: 31.03.2011 Revised: 15.07.2011
Citation:
R. E. Kondrashov, A. D. Morozov, “On global behaviour of the solutions of system of two Duffing – Van der Pole equations”, Nelin. Dinam., 7:3 (2011), 437–449
Linking options:
https://www.mathnet.ru/eng/nd269 https://www.mathnet.ru/eng/nd/v7/i3/p437
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Abstract page: | 268 | Full-text PDF : | 113 | References: | 52 | First page: | 1 |
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