Nonlinear resonance of a controllable bistable state potential model induced by correlated color noises
LIU Jian1，HU Bing2，DING Xiaojian1，QIAO Zijian3，ZANG Chuanlai4
1.College of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, China;
2.College of Modern Posts, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
3.College of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China;
4.Department of Electrical Engineering and Information Systems, The University of Tokyo, Tokyo 113-8656, Japan
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 ,MPFT)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。
Abstract：In this paper, we investigate the particle escape process in the controllable bistable state model, which is driven by cross-correlation colored multiplicative noise and white additive noise. The approximate Fokker-Planck equation and mean first-passage time (MPFT) are derived. It is found that the MPFT as a function of the multiplicative color noise intensity and the additive color noise intensity exhibits the single-peak resonance and inverse resonance phenomenon 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.
刘健1，胡冰2，丁晓剑1，谯自健3，臧传来4. 色关联噪声激励可控双稳态势模型的非线性共振研究[J]. 振动与冲击, 2022, 41(10): 72-80.
LIU Jian1，HU Bing2，DING Xiaojian1，QIAO Zijian3，ZANG Chuanlai4. Nonlinear resonance of a controllable bistable state potential model induced by correlated color noises. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(10): 72-80.
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