We derive the correlation functions for 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 an integral method, are provided. Besides the supercycle, we recognise that the fluctuations in the elements of the period-p orbits are colored noise, which have a non-vanishing time correlation. The results also indicate that the stochastic responses will be stationary after a large number of period-p iterations. These analytical results are confirmed by numerical simulations.
|Number of pages||12|
|Journal||Chinese Journal of Physics|
|Publication status||Published - 1999 Dec 1|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)