Exponential decay and scaling laws in noisy chaotic scattering

被引:49
作者
Seoane, Jesus M. [1 ]
Sanjuan, Miguel A. F. [1 ]
机构
[1] Univ Rey Juan Carlos, Dept Fis, Nonlinear Dynam & Chaos Grp, Madrid 28933, Spain
关键词
D O I
10.1016/j.physleta.2007.06.079
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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 Henon-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. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码:110 / 116
页数:7
相关论文
共 38 条
[1]   Wada basins and chaotic invariant sets in the Henon-Heiles system -: art. no. 066208 [J].
Aguirre, J ;
Vallejo, JC ;
Sanjuán, MAF .
PHYSICAL REVIEW E, 2001, 64 (06) :11
[2]   Unpredictable behavior in the Duffing oscillator:: Wada basins [J].
Aguirre, J ;
Sanjuán, MAF .
PHYSICA D-NONLINEAR PHENOMENA, 2002, 171 (1-2) :41-51
[3]  
[Anonymous], 1993, CHAOS FOCUS ISSUE, V3
[4]   BIFURCATION TO CHAOTIC SCATTERING [J].
BLEHER, S ;
GREBOGI, C ;
OTT, E .
PHYSICA D, 1990, 46 (01) :87-121
[5]  
Burden RL, 1997, NUMERICAL ANAL
[6]   CORRELATION-PROPERTIES OF DYNAMICAL CHAOS IN HAMILTONIAN-SYSTEMS [J].
CHIRIKOV, BV ;
SHEPELYANSKY, DL .
PHYSICA D, 1984, 13 (03) :395-400
[7]  
CONTOPOULOS G, 1990, ASTRON ASTROPHYS, V231, P41
[8]   TRANSITION TO CHAOTIC SCATTERING [J].
DING, M ;
GREBOGI, C ;
OTT, E ;
YORKE, JA .
PHYSICAL REVIEW A, 1990, 42 (12) :7025-7040
[9]  
Do Y, 2004, PHYS REV E, V70, DOI 10.1103/PhysRevE.70.036203
[10]   Superpersistent chaotic transients in physical space: Advective dynamics of inertial particles in open chaotic flows under noise [J].
Do, Y ;
Lai, YC .
PHYSICAL REVIEW LETTERS, 2003, 91 (22)