Exponential decay and scaling laws in noisy chaotic scattering. (English) Zbl 1217.70020
Summary: In this letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Hénon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.
MSC:
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 70H05 | Hamilton’s equations |
| 34K50 | Stochastic functional-differential equations |
| 60H40 | White noise theory |
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