The impact of memory effect on resonance behavior in a fractional oscillator with small time delay

Abstract

We study stochastic resonance (SR) phenomenon in the fractional oscillator with time delay and damping fluctuation, analyze the impact of time delay and fractional damping as two memory ingredients on SR, and put forward firstly the concept of the robustness of GSR. By moment method, we obtain the analytical expression of the output amplitude gain and find that fluctuations in the output amplitude gain are non-monotonic. Using numerical simulations we verify the accuracy of the analytical results. We find (i) that the length of time delay and system order are parameters related to memory; (ii) that the output amplitude gain could attain a maximum by increasing driving frequency close to system frequency, and small time delay and system order contribute to enhance the resonance intensity; (iii) that the evolution of the output amplitude gain versus the noise intensity exhibits one-peak resonance, and small time delay can enhance the resonance intensity and the robustness of SR regarding to driving frequency and system frequency; (iv) that the evolution of the output amplitude gain versus the noise correlation rate presents one-peak resonance in the presence of small time delay, critical time delay is bigger with the increasing system order when noise intensity is fixed and critical time delay is smaller with the increasing noise intensity when system order is fixed.