具有质量及频率涨落的欠阻尼线性谐振子的随机共振∗

摘要

When Brownian particle moves in a viscoelastic medium, the surrounding molecules not only collide with the Brownian particle but also adhere to the Brownian particle randomly, thereby changing the mass of the Brownian particle. We investigate the stochastic resonance phenomenon in an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency under an external periodic force. The exact expressions of the first moment and the amplitude of the output signal are obtained by using the Shapiro-Loginov formula and the Laplace transform technique. We establish the necessary and sufficient conditions for the emergence of the stochastic resonance phenomenon induced by the mass fluctuation noise intensity and frequency fluctuation noise intensity. Furthermore, based on the necessary and sufficient conditions, the output amplitude shows a non-monotonic dependence on the noise intensity, which means that the stochastic resonance phenomenon happens.%以往的研究大多考虑线性谐振子模型受频率涨落噪声的影响，而当布朗粒子处于具有吸附能力的复杂环境时，粒子质量也存在随机涨落。因此，本文研究具有质量及频率涨落两项噪声的二阶欠阻尼线性谐振子模型的随机共振现象。利用Shapiro-Loginov公式和Laplace变换，推导了系统响应一阶稳态矩及稳态响应振幅的解析表达式。并根据稳态响应振幅的解析表达式，建立了稳态响应振幅关于质量涨落噪声及频率涨落噪声各自的噪声强度能够诱导随机共振现象产生的充分必要条件。仿真实验表明，当系统参数满足本文所给出的充分必要条件要求时，系统稳态响应振幅关于噪声强度的变化曲线具有明显的共振峰，即此选定参数组合能够诱导系统产生随机共振现象。