Abstract:In this paper, stochastic resonance (SR) of time-delayed fractional oscillators subjected to both frequency fluctuation and signal-modulated noise is investigated. By using the (fractional) Shapiro-Loginov formula and Laplace transform technique, analytical expression of the output amplitude gain (OAG) is firstly derived, and the dependence of OAG on the system parameters such as the fractional order, time delay and the parameters of noises is explored. It is shown that every dependence is non-monotonic, say, generalized stochastic resonance (GSR) happens. Particularly, the cooperation of fractional order and time delay may result in diverse GSR behaviors. In other word, the GSR behaviors can be controlled by the system parameters.
