|
This article is cited in 3 scientific papers (total in 3 papers)
Mathematical problems of nonlinearity
Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation
A. D. Morozov, K. E. Morozov Lobachevsky State University of Nizhni Novgorod,
prosp. Gagarina 23, Nizhni Novgorod 603950, Russia
Abstract:
We study quasi-periodic nonconservative perturbations of two-dimensional Hamiltonian systems. We suppose that there exists a region $D$ filled with closed phase curves of the unperturbed system and consider the problem of global dynamics in $D$. The investigation includes examining the behavior of solutions both in $D$ (the existence of invariant tori, the finiteness of the set of splittable energy levels) and in a neighborhood of the unperturbed separatrix (splitting of the separatrix manifolds). The conditions for the existence of homoclinic solutions are stated. We illustrate the research with the Duffing – Van der Pole equation as an example.
Keywords:
resonances, quasi-periodic, periodic, averaged system, phase curves, equilibrium states, limit cycles, separatrix manifolds.
Received: 14.04.2019 Accepted: 20.06.2019
Citation:
A. D. Morozov, K. E. Morozov, “Global Dynamics of Systems Close to Hamiltonian Ones Under Nonconservative Quasi-periodic Perturbation”, Rus. J. Nonlin. Dyn., 15:2 (2019), 187–198
Linking options:
https://www.mathnet.ru/eng/nd652 https://www.mathnet.ru/eng/nd/v15/i2/p187
|
Statistics & downloads: |
Abstract page: | 228 | Full-text PDF : | 56 | References: | 30 |
|