SYNCHRONIZATION IN COMPLETE NETWORKS OF ORDINARY DIFFERENTIAL EQUATIONS OF FITZHUGH-NAGUMO TYPE WITH NONLINEAR COUPLING

Abstract

Synchronization is a ubiquitous feature in many natural systems and nonlinear science. This paper studies the synchronization in a complete network consisting of n nodes. Each node is connected to all other nodes by nonlinear coupling and represented by an ordinary differential system of FitzHugh-Nagumo type (FHN) which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, a sufficient condition on the coupling strength is identified to achieve the synchronization. The result shows that the networks with bigger in-degrees of the nodes synchronize more easily. The paper also shows this theoretical result numerically and see that there is a compromise.