Abstract
In this study, the system with fractional power nonlinearity is introduced into the theory of aperiodic stochastic resonance (ASR). The fractional exponent is a key parameter and its effect on the ASR phenomenon excited by aperiodic binary signal is investigated in this system. Compared to the classical bistable system, the system with fractional power nonlinearity shows better performance. It can adjust not only the noise intensity but also the fractional exponent to enhance weak signal. In the field of signal transmission, pure aperiodic binary signal is usually submerged in the noise and the signal is unknown. Thus, an effective method is proposed based on ASR and moving average. By the method, the unknown aperiodic binary signal can be recovered in the noise background. To improve the efficiency of the signal recovery, the adaptive ASR is realised with the help of adaptive particle swarm optimisation (APSO) algorithm to optimise the parameters. The method may provide some reference to the engineering field.
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