具阻尼涨落的时滞分数阶耦合谐振子系统的随机共振

Stochastic resonance in a coupled fractional harmonic oscillators system with time-delay and fluctuating damping

摘要

本文研究了具有阻尼涨落的时滞分数阶耦合谐振子系统的随机共振。利用小延迟近似法和随机平均法，本文得到了两个振子演化行为的完全同步性，从而将对系统平均场演化行为的研究转化为对单个振子演化行为的研究。本文推导了平均场的稳态响应振幅增益（Output Amplitude Gain， OAG）的解析表达式，然后以此为指标讨论了噪声、时滞、耦合、分数阶及驱动等对系统随机共振的影响。主要结果如下：（i） OAG对噪声的强度、相关率和驱动频率均存在非单调依赖，随机共振出现；（ii） 在时滞、耦合和分数阶的共同作用下，系统不但出现多种随机共振，而且这些成分还能增强随机共振。

Abstract

In this paper， the stochastic resonance （SR） in a coupled fractional harmonic oscillators system with fluctuating damping is investigated in the presence of time-delay.By using the small delay approximation and stochastic averaging methods， the complete synchronization of the oscillators is obtained， which allows us to study the dynamical behaviors of mean-field of system through the dynamical behaviors of individual oscillator.Analytic expression for the output amplitude gain （OAG） of the mean-field is obtained.By using OAG as the measure， the effects of noise， time-delay， coupling， fractional order and driving force on the SR of system are addressed.The main results are as follows.（i） There are non-monotonic dependences of OAG on the noise intensity， the driving frequency and the noise correlation rate， which indicates the presence of generalized stochastic resonance （GSR）.（ii） The cooperation of time-delay， fractional order and coupling strength can not only induce diverse GSR behaviors， but also enhance the SR of system.

关键词

随机共振 / 时滞 / 阻尼涨落 / 分数阶耦合谐振子系统

Key words

stochastic resonance / time-delay / fluctuating damping / coupled fractional harmonic oscillators system

基金资助

国家自然科学基金(12471503)

四川省优质研究生教改项目(YJGXM25-C067)

西南石油大学研究生教研教改项目(2024JGZD027)