Logical stochastic resonance in a cross-bifurcation nonsmooth system

Abstract

Abstract This paper investigates logical stochastic resonance (LSR) in a cross-bifurcation non-smooth system driven by Gaussian colored noise. In this system a bifurcation parameter triggers a transition between monostability, bistability and tristability. Using the Novikov’s theorem and the unified colored noise approximation method, the approximate Fokker-Planck equation is obtained. Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon with numerical simulations. We simulate the logical operation of the system in the bistable and tristable regions respectively. We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of logical response depends on noise strength and bifurcation parameter. Furthermore, it is found that the bistable region has a more extensive range of the parameter to produce reliable logic operation compared to the tristable region since the tristable region is more sensitive to noise than the bistable one.