Stochastic resonance in an under-damped linear system with nonlinear frequency fluctuation

Stochastic resonance (SR) in a second-order under-damped linear system with nonlinear frequency fluctuation is investigated, and the nonlinear frequency fluctuation is modeled as dichotomous noise. Firstly, by the use of the Shapiro-Loginov formula and the Laplace transform technique, the analytical expression for the average amplitude gain of the system output is obtained. Then, the non-monotonic behaviors of the average amplitude gain are analyzed. Finally, numerical simulations are presented to verify the effectiveness of the analytical results. Simulation results show that, with the variations of system parameters and noise parameters, the average amplitude gain shows SR and multi-SR phenomena. In addition, the bona fide resonance can be observed by adjusting the frequency fluctuation coefficients. In conclusion all the results show that the nonlinear character of frequency fluctuation plays a key role in system's resonance behavior. Therefore, by introducing nonlinear frequency fluctuation into the linear system, we can control SR in the system in a certain range, and it has promising feasibility in practical engineering application. (C) 2018 Elsevier B.V. All rights reserved.