Theoretical analysis of array-enhanced stochastic resonance in the diffusively coupled FitzHugh-Nagumo equation

Abstract

The array-enhanced stochastic resonance (AESR) in the diffusively coupled FitzHugh-Nagumo equation is investigated. The two properties of AESR, namely, the scaling of the optimal noise intensity and the enhancement of the maximum value of the correlation coefficient as a function of the coupling strength, are analyzed theoretically. By transforming the dynamics of N elements into that of the mean and the deviation from it, it is found that AESR is caused by the correlation between them. A low-dimensional model that reproduces the above properties is constructed.