Stochastic resonance in an ensemble of bistable systems under stable distribution noises and nonhomogeneous coupling

Abstract

In this paper, stochastic resonance of an ensemble of coupled bistable systems driven by noise having an α-stable distribution and nonhomogeneous coupling is investigated. The α-stable distribution considered here is characterized by four intrinsic parameters: α∈(0,2] is called the stability parameter for describing the asymptotic behavior of stable densities; β∈[-1,1] is a skewness parameter for measuring asymmetry; γ∈(0,∞) is a scale parameter for measuring the width of the distribution; and δ∈(-∞,∞) is a location parameter for representing the mean value. It is demonstrated that the resonant behavior is optimized by an intermediate value of the diversity in coupling strengths. We show that the stability parameter α and the scale parameter γ can be well selected to generate resonant effects in response to external signals. In addition, the interplay between the skewness parameter β and the location parameter δ on the resonance effects is also studied. We further show that the asymmetry of a Lévy α-stable distribution resulting from the skewness parameter β and the location parameter δ can enhance the resonance effects. Both theoretical analysis and simulation are presented to verify the results of this paper.