Generalized stochastic resonance in a time-delay fractional oscillator with damping fluctuation and signal-modulated noise

Abstract

In this study, we propose a time-delayed fractional oscillator (FO) subjected to damping fluctuation and signal-modulated noise, and investigate the generalized stochastic resonance (GSR) behaviors. By using (fractional) Shapiro–Loginov formula and Laplace transform, we obtain the first-order moment of system stationary state response, and the output amplitude gain (OAG). Based on the analytical results, it is observed that the GSR behaviors widely exist in the system, and they can be effectively controlled by the system parameters, including driving frequency, noise parameters, fractional order and time delay. It is also demonstrated that fractional order and time delay are two effective dimensions to regulate the GSR intensity under different parameter conditions, and the diversity of GSR behaviors mainly depends on the fractional order.