摘要
提出了一种循环噪声驱动下非对称双稳系统驻留时间分布函数的理论计算方法.利用具有分段逃逸速率的两态模型理论,建立分段逃逸速率方程,分段地推导出了驻留时间分布函数的解析表达式.在此基础上,从理论和数值模拟两方面阐明了在非对称性及循环噪声的影响下驻留时间分布函数呈现出反馈结构.研究结果表明:当非对称性、循环噪声的相关强度及循环滞后时间取适当值时均会造成驻留时间分布函数呈现出分段指数衰减现象且在循环滞后时间处出现骤然下降的趋势.随着非对称性的减小,驻留时间分布函数指数衰减的速率加快并出现单调指数衰减现象.分别增大相关强度和循环滞后时间,驻留时间分布函数在循环滞后时间处骤然下降的间距变小.此外,驻留时间分布函数在循环滞后时间处的值会随着噪声强度和相关强度的改变出现极大值,说明系统发生了随机共振现象.
Residence-times distribution function(RTDF),as a distribution function of times between two consecutive switches in a bistable system,is extensively used to characterize the phenomenon of stochastic resonance(SR).However,most of the studies focus on the symmetric bistable systems.As a matter of fact,the majority of asymmetric systems encountered in nature are more universal and practical.Additionally,due to the combination of diverse propagations or transduction mechanisms,noise recycling,constituted by the superposition of a master noise with a secondary component delayed by a time shift t,can be generated while a noise is injected into a system and transmitted across the system.Therefore,an asymmetric system subjected to noise recycling is no longer non-Markovian.As a result,it is essential to take the special correlation of noise recycling into account when studying the transition dynamics of particles,which makes it difficult to obtain the analytical formula of RTDF.To solve the above problem,a theoretical method to calculate the RTDF of an asymmetric bistable system driven by noise recycling is put forward in this paper.By using the two-state model with piecewise escape rate,the piecewise escape rate function can be established,based on which the RTDF is derived theoretically with a piecewise formula.It is emphatically demonstrated theoretically and numerically that the RTDF exhibits a feedback-induced structure due to the asymmetry of system.Meanwhile,the effects of relative strength and recycling lag on the structure of RTDF are investigated theoretically and numerically.The results are shown as follows:when the asymmetry satisfies g>0 and taking g as the appropriate values,the RTDF decays exponentially and exhibits a sharp dip at t=t.Nevertheless,on the contrary,under the condition for g<0,the dip at t=t of RTDF almost disappears and the rate of decay of RTDF turns to increase.When the relative strength and recycling lag take the appropriate values separately,the RTDF displays piecewise exponential decay
作者
吴亚珍
孙中奎
Wu Ya-Zhen;Sun Zhong-Kui(School of Mathematics and Information Technology,Yuncheng University,Yuncheng 044000,China;Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710072,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2020年第12期2-11,共10页
Acta Physica Sinica
基金
国家自然科学基金(批准号:11772254,11742013,61703363)资助的课题.
关键词
循环噪声
非对称双稳系统
驻留时间分布函数
随机共振
noise recycling
asymmetric bistable system
residence-times distribution function
stochastic resonance
