含相关色噪声和周期方波信号的双稳系统的随机共振  

Stochastic resonance in a bistable system with correlated colored noises and periodic square wave signal

作　　者：曾小玲 任芮彬 邓科[1] ZENG Xiao-Ling;REN Rui-Bin;DENG Ke(School of Mathematics,Sichuan University,Chengdu 610064,China;College of Mathematics,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]四川大学数学学院,成都610064 [2]西南交通大学数学学院,成都611756

出　　处：《四川大学学报（自然科学版）》2023年第4期17-24,共8页Journal of Sichuan University(Natural Science Edition)

基　　金：国家重点研发计划(2020YFA0714000)。

摘　　要：本文研究了含相关色噪声和周期方波信号的双稳系统的随机共振(SR).在绝热极限条件下,本文利用统一色噪声逼近(UCNA)法将原系统转化为相关高斯白噪声驱动的新双稳系统,给出其Fokker-Planck方程后基于双态理论推导了系统信噪比(SNR)的表达式.本文分析了势参数、噪声参数及外力参数对信噪比的影响,发现对所有参数随机共振均出现.本研究可望为实际应用提供理论基础.Stochastic resonance(SR)in a bistable system with correlated colored noises and periodic square wave signal is explored.Given the adiabatic limit condition,the original system is transformed into a new bistable system driven by correlated white Gaussian noises by using the unified colored noise approximation(UCNA)method.Then the Fokker-Planck equation is given for the new system and exact expression for the signal-to-noise ratio(SNR)is deduced by virtue of the two-state theory.Finally,dependence of SNR on the system parameters,including the potenial paramaters,the noise parameters and the external force parameters,is analized.It is shown that SR appears for all parameters.The obtained results are expected to provide a theoretical basis for practical applications.

关 键 词：随机共振 相关色噪声 周期方波信号 双稳系统 

分 类 号：O29[理学—应用数学]