Stochastic resonance in coupled star-networks with power-law heterogeneity

Abstract

In this paper, the power-law heterogeneity of the coupling coefficients is proved to have an important influence on the output signal-to-noise ratio (SNR) of the central oscillator in coupled star-network. The network is described by dimensionless Langevin equations subjected to periodic forces and additive noise in a symmetric bistable potential. Creatively, a random variable with power-law-like distribution is constructed to model the heterogeneity of coupling coefficients. It is revealed that the degree of heterogeneity of coupling coefficients can be measured by the entropy of random variables. In numerical simulation, the output SNR of the central oscillator is obtained to divide the two-dimensional parameter space into four regions of resonance, non-resonance, sub-resonance and super-resonance. In each region, the monotonicity of output SNR curves is discussed to determine the optimal SNR and the corresponding power exponent. At last, an explanation of physical mechanism is given based on the stochastic resonance (SR) theory.