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首页> 外文期刊>Journal of Statistical Physics >Generalized Stochastic Resonance for a Fractional Noisy Oscillator with Random Mass and Random Damping
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Generalized Stochastic Resonance for a Fractional Noisy Oscillator with Random Mass and Random Damping

机译：随机质量和随机阻尼的分数嘈杂振荡器的广义随机共振

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摘要

In this paper, we consider the random dichotomous fluctuations on both mass and damping in a fractional oscillator, which is subjected to an additive fractional Gaussian noise and driven by a periodic force. In order to investigate the generalized stochastic resonance (GSR) phenomena, we acquire the exact expression of the first-order moment of system's steady response by applying generalized fractional Shapiro-Loginov formula and Laplace transform. Meanwhile, we discuss the evolutions of the output amplitude amplification (OAA) with driving frequency, noise parameters, fractional order, and damping strength. It is observed that the non-monotonic resonance behaviors of one-peak GSR, double-peak GSR and triple-peak GSR existing in this fractional system. Moreover, the interplay of mass fluctuation, damping fluctuation, and memory effect can generate a rich variety of non-equilibrium cooperation phenomena, especially the stochastic multi-resonance (SMR) behaviors. It is worth emphasizing that the triple-peak GSR was not observed in previously proposed fractional oscillator subjected to dichotomous noise. Finally, the numerical simulations are also carried out based on predictor-corrector approach to verify the effectiveness of analytic result.
机译：在本文中，我们考虑了在分数振荡器中对质量和阻尼的随机二分波动，其经受添加剂分数高斯噪声并由周期性推动。为了调查广义随机共振（GSR）现象，我们通过应用广义分数Shapiro-Loginov公式和拉普拉斯变换来获得一阶动态稳定响应的精确表达。同时，我们讨论了输出幅度放大（OAA）的演变，驱动频率，噪声参数，分数顺序和阻尼强度。观察到在该分数系统中存在的单调GSR，双峰GSR和三峰GSR的非单调共振行为。此外，质量波动，阻尼波动和记忆效果的相互作用可以产生丰富的非平衡协作现象，特别是随机多共振（SMR）行为。值得强调的是，在先前提出的分数振荡器中未观察到三峰GSR。最后，还基于预测器校正器方法进行数值模拟，以验证分析结果的有效性。

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