Patterns in coupled FitzHugh–Nagumo model on duplex networks

Abstract

Patterns out of homogeneous equilibrium on monolayer networks have been well-documented. However, it is a challenge to understand patterns on multiplex networks. In this work, we study coupled FitzHugh–Nagumo model on duplex networks consisting of two layers. By numerical investigations, we find that the emergent patterns may be characterized by dominant network modes when the homogeneous equilibrium becomes unstable. These dominant network modes on duplex networks are related to the most unstable network modes in monolayer networks. Using these dominant networks modes, we develop approximation methods to deal with the instability of the homogeneous equilibrium on duplex networks. The comparison between theoretical and numerical results suggests that the approximation methods may serve as a tool for analyzing patterns on duplex networks.