Control of synchronization in two delay-coupled FitzHugh-Nagumo systems with heterogeneities

Abstract

We study synchronization in two delay-coupled FitzHugh-Nagumo systems with heterogeneities, which are the simplest model of neural network. It is known that heterogeneities in the network nodes hinder synchronization when becoming too large. We show that external stimulus can be used to counteract the effect of the heterogeneity. We develop two algorithms for synchronization of FitzHugh-Nagumo systems and find the conditions of their applicability. The first algorithm provides synchronization in the case, when all parameters are known and measurable, while the second one is an adaptive controller and is used in the case with uncertain parameters of the system.