On the influence of noise on chaos in nearly Hamiltonian systems

Details On the influence of noise on chaos in nearly Hamiltonian systems On the influence of noise on chaos in nearly Hamiltonian systems

2003-06-16

arxiv.org/abs/nlin/0306024v1

Nonlinear Sciences

Chaotic Dynamics

10 pages REVTEX, 9 figures EPS

Scientific paper

10.1103/PhysRevE.69.026205

The simultaneous influence of small damping and white noise on Hamiltonian systems with chaotic motion is studied on the model of periodically kicked rotor. In the region of parameters where damping alone turns the motion into regular, the level of noise that can restore the chaos is studied. This restoration is created by two mechanisms: by fluctuation induced transfer of the phase trajectory to domains of local instability, that can be described by the averaging of the local instability index, and by destabilization of motion within the islands of stability by fluctuation induced parametric modulation of the stability matrix, that can be described by the methods developed in the theory of Anderson localization in one-dimensional systems.

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