Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices

Soskin, S. M. and Mannella, R. and Yevtushenko, O. M. (2008) Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices. Physical Review E, 77 (3). ISSN 1539-3755

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Abstract

We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.

Item Type:
Journal Article
Journal or Publication Title:
Physical Review E
Additional Information:
©2008 The American Physical Society
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100/3104
Subjects:
ID Code:
73722
Deposited By:
Deposited On:
18 Jun 2015 05:42
Refereed?:
Yes
Published?:
Published
Last Modified:
03 Dec 2020 02:24