具有质量涨落的双分数阶耦合谐振子系统的随机共振

Stochastic resonance of a double fractional coupled harmonic oscillator with mass fluctuation

摘要:

本文对具有质量涨落的双分数阶耦合振子系统的随机共振（Stochastic Resonance，SR）进行了研究. 在利用Shapiro-Loginov公式和Laplace变换求得系统输出振幅增益（output Amplitude Gain，OAG）的解析式后，本文研究了不同参数对OAG共振行为的影响. 数值模拟结果显示，OAG随噪声强度、信号频率及阻尼系数的变化出现随机共振. 此外，分数阶和耦合系数对OAG的随机共振也有影响.

Abstract:

This paper explores the stochastic resonance (SR) of a coupled fractional harmonic oscillator system with mass fluctuation. The Shapiro-Loginov formula and Laplace transform are applied to obtain the analytical expression of the output amplitude gain (OAG) of the system, and the dependence of OAG on the system parameters are studied. Numerical simulation shows that the SR of OAG can be induced by the strength of noise, the signal frequency and the damping intensity. Meanwhile, the fractional order and coupling parameter have an impact on the SR of OAG as well.