Detecting and quantifying stochastic resonance in a coupled fractional-order bistable system driven by Lévy noises via statistical complexity measure

Abstract

In this work, we analyze stochastic resonance phenomenon in two fractional-order bistable systems that are mutually coupled and stimulated by independent Lévy noises. Statistical complexity and normalized Shannon entropy are utilized to characterize stochastic resonance by modulating the parameters of Lévy noise and the given system. It has been determined that the maximum of statistical complexity and minimum of normalized Shannon entropy are regarded as indicators of the severity of dynamical complexity and the occurrence of stochastic resonance, at an optimal level of noise intensity. Then, the influences of various parameters on stochastic resonance are also revealed by the statistical complexity measures. The numerical results demonstrate that the appropriate coupling strength can be found to enhance stochastic resonance effect. The consistency of the complexity of two subsystems is positively correlated to the degree of coupling between them. At lower noise levels, there exists an optimal fractional-order derivative that increases complexity of the system and makes stochastic resonance phenomenon more pronounced. At higher noise levels, the fractional-order derivative suppresses the appearance of stochastic resonance by rendering the evolution of system completely random. Furthermore, stochastic resonance is bolstered by increasing the amplitude of the external periodic signal and stability index, while it is weakened by a larger skewness parameter.