Logical stochastic resonance in a nonlinear fractional-order system

Abstract

We investigate logical stochastic resonance (LSR) in a nonlinear fractional-order system with an asymmetric bistable potential function. We use the success probability of the logical output to measure the logical operation ability of the system. If the success probability is 1, the logical output presents reliable LSR completely. When there are only two logical signals existing in the excitation, LSR can be realized by varying the value of the fractional order or the bias of the potential function. If the fractional order is relatively large, the system performs correct logical operations more easily. With the increase in the bias, the interval of the fractional order corresponding to LSR increases first and then decreases. When both logical signals and Gaussian white noise exist in the excitation, the intervals of the fractional order and the bias corresponding to LSR decrease with the increase in the noise intensity. In addition, with the increase in the value of the fractional order, the maximal value of the success probability also increases. Further, the system usually performs more accurate logical operations when the value of the fractional order lies in the interval [1, 1.5]. The results expand the achievements of LSR. They also provide a reference in choosing an optimal system of LSR.