Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Based on the exponential monostable potential, we study an exponential monostable system with time delayed feedback driven by weak periodic signals and additive Gaussian white noises. The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived. The system parameters l and b, time delay tau, feedback strength beta can change the shapes of the potential function. The mean first-passage time (MFPT) is calculated, which plays an extremely important role in the research of particles escape. And the signal-to-noise ratio (SNR) of the system can be obtained by using the adiabatic approximation theory. The phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback. The amplitude of SNR can be changed by adjusting the system parameters. When the feedback strength beta is positive (or negative), the time delay tau can promote (or suppress) the stochastic resonance phenomenon. The SNR versus the noise intensity D presents the stochastic resonance phenomenon. In addition, the SNR increases non-monotonically with the increasing feedback strength beta and the parameter b. Also, the analysis and numerical simulation results of SNR are in good agreement with the formula simulation. (C) 2018 Elsevier B.V. All rights reserved.