Nonlinear effect of time delay on the generalized stochastic resonance in a fractional oscillator with multiplicative polynomial noise

Abstract

We investigate generalized stochastic resonance (GSR) in a fractional harmonic oscillator with time delay and fluctuation damping. Considering that nonlinear noise widely exists in actual systems compared with linear noise, the fluctuation of damping is modeled as polynomial trichotomous noise. The analytical expression of the output amplitude gain is derived by applying small delay approximation and stochastic averaging. Simulation results show that the output amplitude gain curves, as functions of time delay versus noise parameters, behave non-monotonically and exhibit typical GSR. Furthermore, nonlinear phenomena of stochastic multi-resonance with two, three, and four peaks are observed. Finally, we provide the phase diagrams for GSR versus time delay with different system parameters. Furthermore, the mechanism underlying the stochastic multi-resonance with two, three, and four peaks, as well as their connections, is elucidated. This study could serve as a theoretical basis for the practical use and control of GSR in future works.