Stochastic resonance in coupled fractional-order linear harmonic oscillators with damping fluctuation

Abstract

The stochastic resonance (SR) in the coupled linear harmonic oscillators system containing the fractional-order damping with random dichotomous fluctuation is investigated in this paper. Firstly, by using the mathematical properties of the dichotomous noise, the Shapiro–Loginov formula and the stochastic averaging method, the first moment of the two particles are verified to be equal. Secondly, the analytic expression of the output amplitude gain (G) of the coupled oscillators system is obtained by the Laplace transform method. Thirdly, the numerical simulation results corresponding to the analytic expression show that the fractional-order, coupling coefficient, and damping coefficient all have a great influence on G of the system. Meanwhile, the double stochastic resonances (DSR), parameter-induced stochastic resonance (PSR) and bona-fide resonance (BFR) are discussed based on numerical simulation. Finally, the accuracy of the analytic expression of G has been verified by numerical simulation using the stochastic Euler algorithm.