Aperiodic Stochastic Resonance in the Fractional-Order Bistable System

The aperiodic stochastic resonance (ASR) in the bistable fractional-order system is further studied when the fractional-order lies in the interval (0, 2). In previous works, the ASR can only process aperiodic binary signal with large pulse width. However, for the signal with small pulse width, the method cannot work. Actually, the signals with small pulse width are also common in the information transmission field. It greatly limits the application of the fractional stochastic resonance. Hence, we mainly focus on the enhancement of aperiodic binary signal with small pulse width. To solve the aforementioned technical problem, the general scale transformation is introduced, which allows us to achieve the ASR successfully. By this method, the equivalent system with large system parameters is able to match the input character signal with arbitrary small pulse width well, where the scale parameter is a key to achieve resonance. During the process, the fractional-order system presents rich dynamical behaviors in processing the aperiodic binary signals. Especially, as the order increases, the output signal at optimal noise intensity might be better and be more similar to the input one. This indicates the fractional order can optimize the stochastic resonance. The results might provide some reference to the engineering field, such as digital transmission and image processing field.