Stochastic Resonance in a Bistable System with Time-Delayed Feedback Loops

• 出 处: Communications in Theoretical Physics
• 发表日期: 2008年08期
• 关键词: stochastic Feedback multiplicative helpful discussion unified quantify applying

The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplicative Gaussian coloured noise and additive Gaussian white noise is investigated.Firstly,the analytic expression of the quasi-steady distribution function Ps(x,t) is derived by applying the unified eoloured noise approximation and the Novikov Theorem;Secondly,the expression of the signal-to-noise ratio (SNR) is obtained in the adiabatic limit to quantify the stochastic resonance.Finally,the effects of the linear coefficient a,the nonlinear coefficient b,the linear time-delayed feedback coefficient c and the delay time τ on P_s(x,t) and SNR~± are discussed.It is found that the effects of the linear coefficient and the nonlinear coefficient,the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient,the positive delayed time and the negative delayed time on P_s(x,t) and SNR~± are different,respectively.This discussion would be helpful to the study of the system reliability and controlling stochastic resonance. The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplicative Gaussian colored noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps (x, t) is derived by the unified eolored noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio (SNR) is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, the effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time τ on P_s (x, t) and SNR ~ ± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on P_s (x, t) and SNR ~ ± are different respective ly.This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.