161,235 research outputs found
Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices
No full textWe 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
A new approach to the treatment of separatrix chaos
No full textWe review an approach to separatrix chaos that has allowed us to solve some significant problems by: (i) finding analytically the maximum width of the chaotic layer, a problem that lay unsolved for 40 years, and showing that the maximum may be much larger than had previously been assumed; (ii) describing the drastic facilitation of the onset of global chaos between neighboring separatrices, a phenomenon discovered eight years ago
A new approach to the treatment of Separatrix Chaos and its applications
No full textWe consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe
new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the
size of the low-dimensional stochastic web
Adiabatic divergence of the chaotic layer width and acceleration of chaotic and noise-induced transport
No full textSUMMARY We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold
Adiabatic ac-drive as a tool for acceleration of diffusion in spatially periodic structures and of reset process in threshold devices
No full textDrastic facilitation of the onset of global chaos due to an extremum in the dependence of eigenfrequency on energy
No full textTheory for the drastic facilitation of the onset of global chaos between separatrices of a Hamiltonian system
No full text
Acceleration of the chaotic and noise-induced transport in adiabatically driven spatially periodic systems
No full textWidth of the chaotic layer associated with a separatrix of a one-dimensional Hamiltonian system subjected to a low-frequency time-periodic perturbation
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