Pattern Analysis in Networks of Delayed Coupled Nonlinear Systems

In this paper, a method for pattern analysis in networks of nonlinear systems of Lur'e type interconnected via time-delayed coupling functions is presented. We consider a class of nonlinear systems which are globally asymptotically stable in isolation. Interconnecting such systems into a network via time-delayed coupling can result in persistent oscillatory behavior, which may lead to pattern formation in the delay-coupled systems. We focus on networks of Lur'e systems in which a Hopf bifurcation causes the instability of the network equilibrium. We develop a numerically efficient method in order to analyze the oscillatory behavior occurring in such networks. Our analysis is based on the harmonic balance method and tested on the network of delay coupled FitzHugh-Nagumo (FHN) model neurons.