Stochastic time-delayed systems driven by correlated noises: Steady-state analysis

Huiqing Zhang, Wei Xu, Yong Xu, Dongxi Li

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In the present paper, a class of stochastic time-delayed systems driven by correlated Gaussian white noises are considered. Novikov's theorem is used to derive delay Fokker-Planck equations. In the case of small time delays, approximate stationary solutions are obtained. As a special case, the delay Fokker-Planck equation and the approximate stationary probability density function is obtained for a bistable system. Numerical simulations show that the small-delay approximation is a good approximation in the case of small delay. Furthermore, the effects of the correlated noises and the feedback are investigated. The critical curve separating the unimodal and bimodal regions of the stationary probability distribution is shown to be affected by λ (the degree of the correlation of the noises) and ε (the strength of the feedback). Both λ and ε can change the curve of the stationary probability density function from a bimodal to a unimodal structure.

Original languageEnglish
Pages (from-to)3017-3023
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume388
Issue number15-16
DOIs
StatePublished - 2009

Keywords

  • Delay Fokker-Planck equation
  • Gaussian white noise
  • Time delayed stochastic systems

Fingerprint

Dive into the research topics of 'Stochastic time-delayed systems driven by correlated noises: Steady-state analysis'. Together they form a unique fingerprint.

Cite this