Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

<正>The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C(s).Three cases including linear delay,cubic delay and global delay in the system are considered respectively.The simulation results indicate that the linear delay enhances the fluctuation of the system (reduces the stability of the system) while the cubic delay and global delay weaken it(enforce the stability of the system),and the effect of cubic delay is more pronounced than the linear delay and global delay.     

染料激光色立方模型的第一通过时间分布

本文首先把Ｊｕｎｇ和Ｈａｎｇｇｉ提出的统一色噪声近似推广到多维情形，从而导出了这一近似下单模染料激光色立方模型的朗之万方程和福克－普朗克方程；得到了该模型第一通过时间分布的平均值，协方差和偏斜率的近似解析式并将其和数值模拟进行比较。     

Stochastic Resonance in the Tumour Cell Growth Model

The phenomenon of stochastic resonance （SR） in the tumour cell growth model subjected cross-correlated noises is investigated. When a weakly periodic signal is added to the system, the signal-to-noise ratio RSNR is derived by the quasi-steady-state probability distribution function and the adiabatic elimination method. Based on the derived RSNR, the effects of these parameters （the cross-correlated strength λ and the cross-correlated time τ） are analysed by numerical calculation. It is found that the existence of a maximum in RSNR is the identifying characteristic of the SR phenomenon. The maximum of RsNR decreases with the increase of λ and increases with the increase of τ.