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.