具有随机黏性阻尼的分数维线性振荡器中的随机多共振  

Stochastic Multiresonane for a Fractional Linear Oscillator with Random Viscous Damping Coefficient

作　　者：郭筱瑛 周英姿 王利华 王诗心 Guo Xiaoying;Zhou Yingzi;Wang Lihua;Wang Shixin(School of Intelligent Manufacturing,Panzhihua University,Panzhihua,617000;School of Electrical Engineering and Electronic Information,Xihua University,Chengdu,610039,China)

机构地区：[1]攀枝花学院智能制造学院,攀枝花617000 [2]西华大学电气与电子信息学院,成都610039

出　　处：《电工技术学报》2021年第3期532-541,共10页Transactions of China Electrotechnical Society

基　　金：攀枝花市科研平台及科研团队建设资助项目(攀科知[2017]76号)。

摘　　要：分数阶微积分具有对历史状态的动态记忆特性和路径依赖性等优良特性,因此实际中许多系统,特别是那些具有记忆的动力学过程,用分数阶模型比通常使用的整数阶模型更加合适。在分数阶系统的研究中,采用Gamma函数的记忆核函数是采用Mittag-Leffler函数的记忆核函数的一个特例,而后者更具一般性,特别是其中包含系统特征记忆时间,可以在复杂无序的非均匀环境中描述介质分子对系统运动产生的记忆效应。因此采用Mittag-Leffler函数的分数维导数可以从特征记忆时间和分数维数两个维度更好地刻画系统的性能。该文研究了具有随机黏性阻尼的分数维线性振荡器中的随机多共振现象,分数维振荡器的系统记忆核采用Mittag-Leffler函数。基于线性系统理论,利用Mittag-Leffler函数和分数维导数的性质,推导出系统输出幅度(SPA)的解析表达式。在SPA与分数振荡器记忆时间的关系曲线上发现了随机多共振现象。在SPA与噪声扁平率和黏性阻尼系数的关系曲线上,出现了随机共振效应。SPA随着系统特征频率、驱动信号频率以及噪声相关时间的变化而非单调变化。Fractional calculus has many excellent characteristics,such as dynamic memory of historical state and path dependence.Therefore,for many practical systems,fractional-order models are more suitable to use with comparison to integer-order models,especially for those dynamic processes with memory.In the study of fractional-order systems,the memory kernel function using Gamma function is a special case of that using Mittag-Leffler function.The latter is more general,especially it contains the characteristic memory time of the system,which can describe the memory effect of medium molecules on the system motion in complex and disordered heterogeneous environment.Therefore,the fractional derivative of Mittag-Leffler function can better describe the performance of the system from the two dimensions of characteristic memory time and fractal dimension.In this paper,the stochastic multiresonance for a fractional linear oscillator with random viscous damping coefficient is investigated.The memory kernel of the fractional oscillator is modeled as a Mittag-Leffler function.Based on linear system theory,applying the definition of Mittag-Leffler function and fractional derivative,the expression of the system output amplitude(SPA)is derived.Stochastic multiresonance is found on the SPA curve versus the memory time of the fractional oscillator.Stochastic resonance occurs on the curves of the SPA versus the noise flatness and the viscous damping coefficient.The SPA behaves nonmonotonically with the variety of the system frequency,of the driving frequency,as well as of the noise correlate time.

关 键 词：随机多共振 分数维线性振荡器 随机黏性阻尼 系统输出幅度 

分 类 号：TN911.23[电子电信—通信与信息系统]