Stochastic Responses of the Stable Period-p Orbits in One-Dimensional Noisy Map Systems

Details Stochastic Responses of the Stable Period-p Orbits in One-Dimensional Noisy Map Systems Stochastic Responses of the Stable Period-p Orbits in One-Dimensional Noisy Map Systems

1997-12-23

arxiv.org/abs/chao-dyn/9712019v3

Nonlinear Sciences

Chaotic Dynamics

Latex, 17 pages with 7 figures

Scientific paper

We analytically derive the correlation functions of the stochastic response of period-p orbits in a generic one-dimensional map system under the influence of weak external, additive white noise. Two approaches, a recurrence scheme and a path integral method, are provided. Beside the supercycle, we recognise that the fluctuations on each elements of the period-p orbits are colored noise which have non-vanishing time correlation. The results also indicate that the stochastic responses will be stationary after a large number of period-p iterations. The analytical results are confirmed by numerical simulations.

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