| Summary: | Stochastic resonance on under-damped nonlinear frequency fluctuation for coupled fractional-order linear particles is investigated. First, the average motions of the two coupled Brownian particles obtained by the random average method and the Shapiro-Loginov formula are completely synchronized. Then, on the basis of synchronization, the mathematical formula of the system output amplitude gain of one of the particles is calculated. Numerical simulation results show that there exist various stochastic resonance phenomena with system and noise parameters changing, such as double-peak SR (DSR), bona-fide resonance (BFR), and parameter-induced SR (PSR). The nonlinear noise coefficient plays a significant role in the system. Finally, the accuracy of theoretical analysis is verified by Simulink numerical simulation.
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