Stochastic resonance of underdamped harmonic oscillator with random mass driven by periodic modulated noise

Abstract:

In this paper, stochastic resonance of an underdamped harmonic oscillator with random mass and driven by periodic modulated noise is investigated. The fluctuation of oscillator mass is modeled by a dichotomous noise while the internal noise is assumed to be Gaussian. Using the Shapiro-Loginov formula and the Laplace transform technique, exact expressions of first moment of the steady-state response and output of the system are presented. Then some simulations are implemented to study the dependence of long-time behavior of the first moment on variety of the system parameters. It is shown that the output amplitude non-monotonically depends on the signal frequency, the noise parameters and the system parameters, which indicates the occurrences of bona fide stochastic resonance, generalized stochastic resonance and parameter-induced stochastic resonance. Furthermore, based on the exact expressions it is demonstrated that interplay of the mass fluctuation and the periodic modulated noise can generate some novel cooperation effects, such as double-peak resonance as well as one-valley resonance.