Abstract
The stochastic multiresonance behavior for a fractional linear oscillator with random system frequency is investigated. The fluctuation of the system frequency is a quadratic trichotomous noise, the memory kernel of the fractional oscillator is modeled as a Mittag–Leffler function. Based on linear system theory, applying Laplace transform and the definition of fractional derivative, the expression of the system output amplitude (SPA) is obtained. Stochastic multiresonance phenomenon is found on the curves of SPA versus the memory time and the memory exponent of the fractional oscillator, as well as versus the trichotomous noise amplitude. The SPA depends non-monotonically on the stationary probability of the trichotomous noise, on the viscous damping coefficient and system characteristic frequency of the oscillator, as well as on the driving frequency of external force.
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