Trichotomous noise induced stochastic resonance in a fractional oscillator with random damping and random frequency

In this study, we investigate the stochastic resonance (SR) of a fractional linear oscillator subjected to multiplicative trichotomous noise and additive fractional Gaussian noise and driven by a periodic signal. Using the Shapiro-Loginov formula and the Laplace transformation technique, we acquire the exact expression of the first-order moment of the system's steady response. Meanwhile, we discuss the evolutions of the output amplitude with the frequency of the periodic signal and noise parameters. We determine that bona fide SR, SR and reverse-resonance exist in this system. Specifically, the evolution of the output amplitude with the frequency of the periodic signal presents one-peak oscillation, double-peak oscillation and triple-peak oscillation. Moreover, the interplay of the trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena and give this linear system richer dynamic behavior. A hypersensitive response of the output amplitude to the noise intensity is demonstrated, which is not observed in systems driven by dichotomous noise.