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色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子的共振行为
Resonant behavior of a fractional linear oscillator with fluctuating frequency and periodically modulated noise?
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摘要: 研究了色噪声参激和周期调制噪声外激联合驱动的分数阶线性振子及其共振行为,利用Laplace变换和Shapiro-Loginov公式,推导出了系统响应的一阶矩及稳态响应振幅的解析表达式.讨论了系统阶数、摩擦系数、周期驱动力频率、色噪声强度和相关率等参数对系统稳态响应的影响,发现系统稳态响应振幅具有非单调变化的特点,即出现了广义随机共振现象.并且在适当参数下,稳态响应振幅还存在具有双峰的广义随机共振现象.Abstract: The resonant behavior of a fractional linear oscillator subjected to both parametric excitation of colored noise and external ex-citation of periodically modulated noise is considered. Using Laplace transformation technique and Shapiro-Loginov formula, exact expressions of the first moment for the system response and its long-time amplitude are presented. The influence of the system pa-rameters on the long-time behavior of the system response is discussed, such as fractional order, friction coefficient, driving frequency, noise intensity and relevant rate. It is found that the long-time amplitude of the fractional oscillator behaves non-monotonical, that is, there exist stochastic resonances in a wide sense. Moreover, generalized stochastic resonance with two peaks can be found subject to some appropriate parameters.
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