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

Tian-Nan Wang; Rue-Ron Hsu; Han-Tzong Su; Wei-Fu Lin; Jyh-Long Chern; Chia-Chu Chen

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

chao-dyn 2019-08-17 v3 Chaotic Dynamics

Authors: Tian-Nan Wang , Rue-Ron Hsu , Han-Tzong Su , Wei-Fu Lin , Jyh-Long Chern , Chia-Chu Chen

Abstract

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.

Keywords

stochastic response period-p orbits one-dimensional maps additive white noise correlation functions path integral recurrence scheme colored noise

Cite

@article{arxiv.chao-dyn/9712019,
  title  = {Stochastic Responses of the Stable Period-p Orbits in One-Dimensional Noisy Map Systems},
  author = {Tian-Nan Wang and Rue-Ron Hsu and Han-Tzong Su and Wei-Fu Lin and Jyh-Long Chern and Chia-Chu Chen},
  journal= {arXiv preprint arXiv:chao-dyn/9712019},
  year   = {2019}
}

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Latex, 17 pages with 7 figures

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

Abstract

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