Stochastic resonance in a linear system with random damping parameter driven by trichotomous noise

The stochastic resonance (SR) in a second-order linear system driven by a trichotomous noise and an external periodic signal is investigated. By the use of the properties of the trichotomous noise and the Shapiro-Loginov formula, the exact expression for the output spectral amplification (SPA) of the system is obtained. The non-monotonic influence of the coefficient of the trichotomous noise on the SPA is found. It is shown that the SPA is a non-monotonic function of the amplitude, the correlation rate and the probability of the trichotomous noise. The SPA varies non-monotonically with the frequency of the driving signal, the damping coefficient and the frequency of the linear system.