多稳态动力系统中随机共振的研究进展  

Stochastic resonance of multi-stable dynamical systems:A review

作　　者：靳艳飞[1] 许鹏飞 李永歌[3,5] 马晋忠 许勇[3,5] JIN Yanfei;XU Pengfei;LI Yongge;MA Jinzhong;XU Yong(Department of Mechanics,Beijing Institute of Technology,Beijing 100081,China;Department of Mathematics,Shanxi Agricultural University,Jinzhong 030801,Shanxi,China;School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710072,China;School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China;MOE Key Laboratory for Complexity Science in Aerospace,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]北京理工大学力学系,北京100081 [2]山西农业大学数学系,山西晋中030801 [3]西北工业大学数学与统计学院,西安710072 [4]山西大学数学科学学院,太原030006 [5]西北工业大学空天领域复杂性科学教育部重点实验室,西安710072

出　　处：《力学进展》2023年第2期357-394,共38页Advances in Mechanics

基　　金：国家自然科学基金资助项目(12072025,12202253,12272296,12120101002);重庆市自然科学基金项目(cstc2021jcyj-msxmX0738);广东省基础与应用基础研究基金用基础研究基金(2023A1515012329)。

摘　　要：非线性随机动力学是力学、数学、工程等多个领域关注的热点,在航空航天、机械工程、生物生态等领域有广泛的应用.多稳态动力系统作为其最重要的研究对象,在随机扰动下具有丰富的动力学行为,如随机分岔、随机共振等,尤其是随机共振,已经被应用于机械故障诊断、微弱信号检测和振动能量俘获等工程实际问题中.本文主要综述了多稳态动力系统中的随机共振理论、方法及工程应用.首先,通过几类典型的非线性随机动力学系统,介绍了随机共振的经典理论和度量指标;其次,重点阐述了多稳态动力学系统,尤其是三稳态和周期势系统,在各类噪声激励下的随机共振现象,分析了其诱发机理、演化规律和研究方法;最后,介绍了多稳态动力系统中随机共振的几类应用实例,并进一步给出了随机共振当前面临的难题和未来的发展趋势等开放性问题.The nonlinear stochastic dynamical system has been an important subject in areas of mechanics,mathematics,engineering and so on,and finds various applications in different fields like mechanical engineering,aerospace engineering,ocean engineering,and biology.The multi-stable dynamical systems are conceptual nonlinear systems,coupling with stochastic excitations,which can exhibit complex dynamical behaviors,such as stochastic resonance and stochastic bifurcation.The stochastic resonance theory has been utilized effectively in many areas related to stochastic dynamics such as mechanical fault diagnosis,weak signal detection and vibration energy harvesting.This paper overviews the fundamental theories,methods and engineering applications of stochastic resonance in multi-stable dynamical systems.We introduce recent advances in theories and measure index of stochastic resonance via several classic examples of nonlinear dynamical systems.Then,we summarize the results of multi-stable dynamical systems under the excitation of different types of noise.The tristable and periodic systems are illustrated to show the occurrence principle,evolution mechanism and investigated techniques.Finally,three engineering applications of multi-stable dynamical systems are surveyed.Some open problems are presented to close this paper.

关 键 词：随机共振 多稳态动力系统 相干共振 平均首次穿越时间 非高斯Lévy噪声 

分 类 号：O324[理学—一般力学与力学基础]