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Correlation functions of an autonomous stochastic system with time delays

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  • Zhu, Ping
  • Mei, Dong Cheng

Abstract

The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function Cx(s) and Cy(s), and the cross-correlation function Cxy(s) and Cyx(s) of the stochastic dynamic variables by the stochastic simulation method. The delay time changes prominently the behaviors of the dynamical variables of an autonomous stochastic system, which makes the auto-correlation and the cross-correlation of the autonomous stochastic system alternate oscillate periodically from positive to negative, or from negative to positive, decrease gradually, and finally tends to zero with the decay time. The delay time and the noise strength have important impacts for the auto-correlation and the cross-correlation of the autonomous stochastic delay system. The delay time enhances the auto-correlation and the cross-correlation, on the contrary, the noise strength lowers the auto-correlation and the cross-correlation. Under the time delay, by comparison we further show differences of the auto-correlation and the cross-correlation between the dynamical variables x and y.

Suggested Citation

  • Zhu, Ping & Mei, Dong Cheng, 2014. "Correlation functions of an autonomous stochastic system with time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 152-161.
    • Handle: RePEc:eee:phsmap:v:398:y:2014:i:c:p:152-161
    DOI: 10.1016/j.physa.2013.12.022
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