含信号调制噪声和频率波动的时滞分数阶振子的随机共振

Stochastic resonance of a time-delayed fractional oscillator with fluctuating frequency and signal-modulated noise

摘要:

本文研究了含信号调制噪声和频率波动的小时滞线性分数阶振子的随机共振. 利用分数阶Shapiro-Loginov公式和Laplace变换技巧，本文首先推导了系统响应的一阶稳态矩和稳态响应振幅增益（Output Amplitude Gain, OAG）的解析表达式，然后讨论了分数阶、时滞及噪声参数对OAG的影响. 结果显示，各参数对OAG的影响均呈现出非单调变化的特点，表明系统出现广义随机共振. 特别地，分数阶与时滞的协同作用可能诱导随机共振的多样化，这就为在一定范围内调控随机共振提供了可能.

Abstract:

In this paper, stochastic resonance (SR) of time-delayed fractional oscillators subjected to both frequency fluctuation and signal-modulated noise is investigated. By using the (fractional) Shapiro-Loginov formula and Laplace transform technique, analytical expression of the output amplitude gain (OAG) is firstly derived, and the dependence of OAG on the system parameters such as the fractional order, time delay and the parameters of noises is explored. It is shown that every dependence is non-monotonic, say, generalized stochastic resonance (GSR) happens. Particularly, the cooperation of fractional order and time delay may result in diverse GSR behaviors. In other word, the GSR behaviors can be controlled by the system parameters.