Controlled synchronization in two hybrid FitzHugh-Nagumo systems

We study synchronization in two FitzHugh-Nagumo systems with discrete coupling, which are the simplest model of neural network. It is well known that high delays in propagation between the nodes hinder synchronization. We use the linear matrix inequality method to study the impact of the discretization step on the system synchronization. We show that external stimulus can be used for controlling synchrony in the case of its absence. We develop the algorithm for synchronization of FitzHugh-Nagumo systems and find the conditions of its applicability. The simulation results confirm the efficiency of suggested algorithm.