色关联噪声激励可控双稳态势模型的非线性共振研究  

Nonlinear resonance of a controllable bistable state potential model induced by correlated color noises

作　　者：刘健 胡冰[2] 丁晓剑 谯自健 臧传来 LIU Jian;HU Bing;DING Xiaojian;QIAO Zijian;ZANG Chuanlai(College of Information Engineering,Nanjing University of Finance and Economics,Nanjing 210023,China;College of Modern Posts,Nanjing University of Posts and Telecommunications,Nanjing 210003,China;College of Mechanical Engineering and Mechanics,Ningbo University,Ningbo 315211,China;Department of Electrical Engineering and Information Systems,The University of Tokyo,Tokyo 113-8656,Japan)

机构地区：[1]南京财经大学信息工程学院,南京210023 [2]南京邮电大学现代邮政学院,南京210003 [3]宁波大学机械工程学院,浙江宁波315211 [4]东京大学电气工程与信息学院,东京113-8656

出　　处：《振动与冲击》2022年第10期72-80,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(62001210);江苏省自然科学基金(BK2019789);浙江省自然科学基金(LQ22E050003);江苏省高等学校自然科学研究项目(19KJB130006)。

摘　　要：研究了色关联乘性色噪声和加性白噪声激励可控双稳态势模型的粒子逃逸过程,推导出近似Fokker-Planck方程和平均首通时间(mean first-passage time,MFPT)表达式,分析可控阱深和可控阱宽下系统参数对平均首通时间的影响。研究结果表明:平均首通时间作为乘性色噪声强度和加性白噪声强度的函数展现出单峰共振和反共振现象,两噪声间的色关联性能激发系统跃迁行为,自(互)关联时间和互关联强度可以诱导系统的共振现象;可控势阱因子对左势阱和右势阱的初始位置逃逸行为的影响不同,能增强可控双稳态势模型稳定性,大尺度可控势阱因子在可控阱宽情形下占据了粒子跃迁行为的主导作用。The particle escape process in a controllable bistable state model was investigated,which was driven by the cross-correlation colored multiplicative noise and white additive noise.The approximate Fokker-Planck equation and mean first-passage time(MFPT)were derived.It is found that the MFPT as a function of the multiplicative color noise intensity and the additive color noise intensity exhibits the single-peak resonance and inverse resonance phenomena and the color correlation between the two noises can stimulate the transition process of the system.The self or corss-correlation time and the cross-correlation strength can induce the resonance phenomenon.The influence of the controllable potential factor on the initial position escape behavior of the left and right wells is different,and it can enhance the stability of the controllable bistable state potential model.The large-scale controllable potential factor occupies the leading role of particle transition behavior in the case of controllable well width.

关 键 词：非线性共振 色关联噪声 可控双稳势模型 粒子跃迁 平均首通时间(MFPT) 

分 类 号：O322[理学—一般力学与力学基础]