具有阻尼涨落的时滞分数阶耦合谐振子的随机共振
Year: 2025
Type: article
Abstract: Time delay exists widely in practical systems. In the presence of time delay, stochastic resonance (SR) in a coupled system of two fractional harmonic oscillators with fluctuating damping is investigated. In this paper, the mean-field of system is the average of trajectories of two oscillators. By using small delay approximation and stochastic averaging method, we firstly find the complete synchronization between the average behaviors of the two oscillators in the presence of time delay, which allows us to study the mean- field of the system through each individual oscillator. Then we obtain the analytic expression of output amplitude gain (OAG) of the mean-field. According to the expression of OAG, we discuss the impact of time delay, system order and coupling strength on OAG. It is shown that the dependence of OAG on noise intensity，driving frequency，noise correlation rate are non-monotonic respectively, which means generalized stochastic resonance (GSR) happens. Particularly, the cooperation of time delay, system order and coupling strength not only diverse GSR behaviors of the system, but also amplify the resonance intensity. These conclusions provide theoretical basis for the appliance of stochastic resonance in weak signal detection. 时滞广泛且普遍地存在于实际系统中，本文研究了时滞存在情形下具有阻尼涨落的由两个分数阶谐振子构成的耦合系统的随机共振行为.本文中系统的平均场为两个耦合振子运动轨迹的算术平均值，利用小延迟近似法和随机平均法，通过推导首先发现了在时滞存在的情况下两个耦合振子的完全同步性，然后得到了平均场的稳态响应振幅增益(OAG)的解析表达式，进而讨论了时滞、耦合强度和系统阶数对OAG的影响。研究结果表明OAG随噪声强度、驱动频率、噪声相关率的变化均可呈现非单调依赖行为，这表明广义随机共振(GSR)出现；时滞、耦合强度和系统阶数的协同作用不仅能诱导随机共振的多样化，还能增强随机共振的强度.本研究为随机共振在弱信号检测中的应用提供理论基础.
Language: Chinese
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162726561