Stochastic resonance in a harmonic oscillator subject to random mass and periodically modulated noise

In many practical systems, the periodic driven force and noise are introduced multiplicatively. However, the corresponding researches only focus on the first order moment of the system and its stochastic resonance phenomena. This paper investigates a harmonic oscillator subject to random mass and periodically modulated noise. Using Shapiro-Loginov formula and the Laplace transformation technique, the analytic expressions of the first-order and second-order moment are obtained. According to the analytic expressions, we find that although the first-order moment is always zero but second-order moment is periodic which is different from other harmonic oscillators investigated. Furthermore, we find the amplitude and average of second-order moment have a non-monotonic behavior on the frequency of the input signal, noise parameters and other system parameters. Finally, the numerical simulations are presented to verify the analytical results.