含记忆阻尼函数的周期势系统随机共振  

Stochastic resonance in periodic potential system with memory damping function

作　　者：许鹏飞 公徐路 李毅伟 靳艳飞[3] Xu Peng-Fei;Gong Xu-Lu;Li Yi-Wei;Jin Yan-Fei(Department of Mathematics,Shanxi Agricultural University,Taigu 030801,China;School of Software,Shanxi Agricultural University,Taigu 030801,China;Department of Mechanics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]山西农业大学数学系,太谷030801 [2]山西农业大学软件学院,太谷030801 [3]北京理工大学力学系,北京100081

出　　处：《物理学报》2022年第8期26-36,共11页Acta Physica Sinica

基　　金：山西省优秀博士来晋工作奖励资金科研项目(批准号:SXBYKY2021081);山西农业大学博士科研启动项目(批准号:2021BQ12);山西农业大学青年科技创新基金(批准号:2019019,2020QC04);北京理工大学研究生教研教改项目资助的课题~~。

摘　　要：研究了外部周期信号和内部噪声共同激励下,含记忆阻尼函数的周期势系统的随机共振.针对具有多稳态特征的周期势系统,推导出适用于一般多稳态模型的系统响应振幅和功率谱放大因子.研究结果表明,功率谱放大因子随温度的变化曲线出现单峰,说明含记忆阻尼函数的周期势系统存在随机共振现象,并且系统的记忆特性和稳态点数量对共振行为有着显著影响.此外,利用随机能量法进一步分析了系统的随机共振现象,发现共振效应随着记忆时间的增加先减弱再增强.在适当的温度条件下,存在最优记忆时间可以最大化外部周期力对系统所做的功.The stochastic dynamical system with memory effects describes a non-Markovian process that can happen in some complex systems or disordered media,such as viscoelastic media and living cell.Its velocity yields the memory effects because of the nonlocality in time,giving rise to a generalized Langevin equation for describing the dynamics of the system.In particular,the friction term in generalized Langevin equation is given by the time-dependent memory kernel.Besides,the research of stochastic resonance in periodic potential models emerges as an important subject because such systems have potential applications in diverse areas of natural sciences.However,the analysis of the influence of memory on stochastic resonance has not been reported so far in periodic potential model.In this paper,the phenomenon of stochastic resonance is investigated in the periodic potential system with friction memory kernel driven by an external periodic signal and internal noise.The generalized Langevin equation is converted into the three-dimensional Markovian Langevin equations.Analytical expression for the spectral amplification,together with the amplitude of the response,is derived in the periodic potential with an arbitrary number of simultaneously stable steady states,which can be applied to the general multi-stable dynamical model.The obtained results indicate that the curve of spectral amplification versus temperature exhibits a pronounced peak.Obviously,this typical phenomenon is a signature of stochastic resonance.The stochastic resonance effect is enhanced with the increase of the memory time or the number of stable steady states.For a certain range of the particle motion,the existence of an optimal number of stable steady states for which the output of the system can be maximized is established.Moreover,the phenomenon of stochastic resonance is studied according to the stochastic energetics.The average input energy per period is calculated over all the trajectories for quantifying stochastic resonance.It is found that the st

关 键 词：随机共振 周期势系统 广义Langevin方程 

分 类 号：O324[理学—一般力学与力学基础]