SUFFICIENT CONDITION FOR GENERALIZED SYNCHRONIZATION IN THE NETWORKS OF TWO ORDINARY DIFFERENTIAL EQUATIONS OF FITZHUGH-NAGUMO TYPE WITH UNIDIRECTIONALLY LINEAR COUPLING

Abstract

In this paper, we study the generalized synchronization in the network of two ordinary differential equations of FitzHugh-Nagumo type with unidirectionally linear coupling. Specifically, we search for sufficient conditions on the coupling strength and construct a synchronous controller to get the generalized synchronization. This paper also presents the simulations for checking the theoretical results. The results show that there is agreement between theoretical results and numerical methods, especially the effectiveness of the constructed synchronous controller in this work.