Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-12-13
Nonlinear Sciences
Chaotic Dynamics
29 pages, 16 figures (figs. are of reduced quality, original files are available on request from authors), paper has been sign
Scientific paper
We have developed the {\it general method} for the description of {\it separatrix chaos}, basing 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 apply the above theory to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered (PRL 90, 174101 (2003)). The theory well agrees with simulations. We also discuss generalizations and applications. Examples of applications of the facilitation include: the increase of the DC conductivity in spatially periodic structures, the reduction of activation barriers for noise-induced transitions and the related acceleration of spatial diffusion, the facilitation of the stochastic web formation in a wave-driven or kicked oscillator.
Mannella Riccardo
Soskin Marat S.
Yevtushenko O. M.
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