Correlation Functions of an Autonomous Stochastic System with Nonlinear Time Delays. (1st February 2015)

• Record Type: Journal Article
• Authors: Zhu, Ping; Zhu, Yi-Jie
• Is Part Of: Communications in theoretical physics. Volume 63:Number 2(2015:Feb.)
• Page Start: 181
• Page End: 187
• Publication Date: 2015-02-01
• Subjects: Physics -- Periodicals; 530.105
• DOI: 10.1088/0253-6102/63/2/10
• Languages: English
• ISSNs: 0253-6102

Abstract

<abstract xml:lang="en"> <title>Abstract</title> <p>The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences between the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonlinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.</p> </abstract>