Lévy噪声和高斯白噪声共同激励的非对称三稳系统的随机共振  

Stochastic resonance of asymmetric tristable systems excited by Lévy noise and Gaussian white noise

作　　者：郭永峰 刘倩茹 张萌 GUO Yongfeng;LIU Qianru;ZHANG Meng(School of Mathematical Science,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《安徽大学学报（自然科学版）》2023年第2期1-9,共9页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11672207);天津市自然科学基金资助项目(17JCYBJC15700)。

摘　　要：将Lévy噪声和高斯白噪声引入非对称三稳系统模型中,采用数值方法计算不同参数下系统的信噪比,分析噪声参数、系统参数以及信号振幅对系统随机共振现象的影响机制.研究结果表明,较大的稳定性指标、偏斜参数、3次刚度系数以及信号振幅会抑制随机共振现象的发生,而较大的非对称参数则会促进随机共振现象的发生.特别地,当信噪比作为加性噪声强度的函数时,较大的5次刚度系数不易于出现随机共振现象,而当信噪比作为乘性噪声强度的函数时,情况则相反,即5次刚度系数越大越容易发生随机共振现象.In this paper,Lévy noise and Gaussian white noise were introduced into the asymmetric tristable system model.Then we calculated signal-to-noise ratio(SNR)of the system with different parameters by numerical method.The influence mechanism of noise parameters,system parameters and signal amplitude on the stochastic resonance(SR)phenomenon of the system were analyzed.And the results showed that the larger stability index,skewness parameter,cubic stiffness coefficient and amplitude all inhibited the occurrence of SR phenomenon.But the increase in asymmetric parameters enhanced the SR phenomenon.In particular,when SNR was studied as a function of additive noise intensity,the larger quintic stiffness coefficient was more difficult to observe the SR phenomenon.However,when SNR was studied as a function of multiplicative noise intensity,the situation was contrary,that was the increase in quintic stiffness coefficient promoted the SR phenomenon of the tristable system.

关 键 词：非对称三稳系统 信噪比 随机共振 Lévy噪声 

分 类 号：O414.2[理学—理论物理] O415.6[理学—物理]