循环噪声作用下周期调制双稳系统的驻留时间分布函数  

Residence-times distribution function of a periodically modulated bistable system subject to noise recycling

作　　者：吴亚珍 孙中奎[1] WU Yazhen;SUN Zhongkui(School of Mathematics and Statistics,Northwestern Polytechnical University,Xi′an 710129,China;School of Math&Information Technology,Yuncheng University,Yuncheng 044000,China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710129 [2]运城学院数学与信息技术学院,山西运城044000

出　　处：《西北工业大学学报》2024年第1期165-172,共8页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(11772254,11972288,12272295);山西省自然科学基金(20210302123082);山西省回国留学人员科研资助项目(2021-149)资助。

摘　　要：提出了一种计算循环噪声作用下周期调制双稳系统驻留时间分布函数的理论方法。基于具有分段逃逸速率的两态模型理论,建立粒子逃逸的瞬时速率方程,推导得出驻留时间分布函数的递归表达式。基于此,分别计算信号振幅与循环噪声强度比值较大和较小2种不同情形下驻留时间分布函数的解析表达式。并且,从理论和数值模拟两方面分别阐明了循环噪声对驻留时间分布函数结构的影响。研究结果表明:驻留时间分布函数呈现指数衰减且在循环滞后时间处出现骤然下降趋势,且随着噪声强度和相关强度的增大驻留时间分布函数衰减速度变快,说明循环噪声能够加速粒子在势阱间的跃迁。此外,在周期信号的调制下,驻留时间分布函数在信号半周期的奇数倍处出现一系列峰值,这预示着系统发生了随机共振现象。The research mentioned in the statement focuses on investigating a theoretical method for calculating the residence-times distribution function(RTDF)in a periodically driven,bistable system subject to noise recycling.This situation deviates from a Markovian process due to the recycling lag,making it challenging to determine the RTDF using traditional two-state models.In this paper,the aim is to overcome this issue and provide a systematic analysis of how to calculate the RTDF in such a system.By considering the piecewise escape rate of the system,which relies not only on the current state but also on the previous state,we have successfully derived the recursive expression of RTDF.Then,RTDF for large and small A/[AKD-]is approximately derived using a piecewise analysis formula,respectively.It is further demonstrated both theoretically and numerically that the RTDF has exhibited a feedback-induced structure as a result of the recycling procedure.The results are shown as follows:for large A/[AKD-],the RTDF exhibits a series of sharp peaks located at odd multiples of approximately half the period of the driving signal.This indicates the occurrence of stochastic resonance.Additionally,it is interesting to note that the RTDF displays a sharp dip at t=τ.It is further shown that the process of noise recycling increases the probability of short residence times for t<τand decreases the probability of long residence times for t>τ.This demonstrates that noise recycling plays a crucial role in facilitating particle hops between the double-well potential.For small A/[AKD-],the RTDF displays a phenomenon of piecewise exponential decay and declines sharply at t=τ.Notably,the interval between discontinuities becomes smaller or even disappears with increasing the noise intensity or the relative strength.Furthermore,when driven by an appropriate periodic signal,the RTDF exhibits a sequence of maximum values at odd multiples of approximately half the period of the driving signal.However,these maximum values disappear with increa

关 键 词：循环噪声 周期调制双稳系统 驻留时间分布函数 随机共振 

分 类 号：O19[理学—数学]