In this paper,we prove some limsup results for increments and lag increments of G(t),which is a stable processe in random scenery.The proofs rely on the tail probability estimation of G(t).
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 differenc...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 be- tween 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 nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.展开更多
文摘In this paper,we prove some limsup results for increments and lag increments of G(t),which is a stable processe in random scenery.The proofs rely on the tail probability estimation of G(t).
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘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 be- tween 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 nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.
