Self-similarity and adaptive aperiodic stochastic resonance in a fractional-order system

Abstract

We investigate the aperiodic stochastic resonance (ASR) in a bistable fractional-order system when the fractional order lies in the interval (0, 2]. We find that a weak aperiodic signal can be amplified and optimized by varying the fractional order in the nonlinear system, no matter whether it has the assistance of the noise or not. We focus mainly on the self-similarity of the response to the input aperiodic signal and the adaptive ASR. The self-similarity is a characteristic that the response of a nonlinear system matches the input signal well, in the absence of the noise excitation. The adaptive ASR is a technique for the optimal ASR to occur by modulating the fractional order, the noise intensity, or the bistable system parameters. In order to make the optimal ASR occur, an adaptive particle swarm optimization (APSO) algorithm is used in this work as the method of parameter optimization. In previous works, only the periodic signal is optimized in a noisy bistable fractional-order system and the ASR induced by the fractional-order system has not been achieved. In engineering and scientific fields, not only periodic signals need to be processed, but also weak aperiodic ones. Moreover, the optimal ASR shows better results based on the APSO algorithm. We believe that the results of this paper might have a positive contribution in the dynamics research.