Resonant behavior of a fractional linear oscillator with fluctuating frequency and periodically modulated noise
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

The resonant behavior of a fractional linear oscillator subjected to both parametric excitation of colored noise and external excitation 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 parameters 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.