<Abstract>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 investi...<Abstract>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.展开更多
基金supported by National Natural Science Foundation of China under Grant Nos.10472091 and 10332030
文摘<Abstract>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.
