Abstract
In this paper, stochastic resonance in a fractional oscillator with a power-law friction kernel subject to random damping is investigated both theoretically and numerically. The influence of a fluctuating damping is modeled as multiplicative trichotomous noise. The exact expression of the first moment of the system $$'$$ s steady response has been calculated. It is shown that the interplay between multiplicative trichotomous noise and memory effect leads to stochastic resonance in the proposed system. The output amplitude gain (OAG) shows non-monotonic dependence on the driving frequency of the input signal and the characteristics of the noise. Furthermore, a multiresonance-like behavior of the OAG as function of the driving frequency and the inverse-stochastic resonance behavior of the OAG as function of the noise switching rate are observed, which is previously reported and believed to be absent in the case of the non-memory oscillator. Finally, some numerical simulations are performed to support the theoretical analyses.
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