Synchronization Analysis of Coupled Fitzhugh Nagumo Dynamical Systems

Synchronization plays a pivotal role in understanding various natural events. Understanding this concept with reference to a biologically inspired dynamical model of a neuron is also essential. It is basically a rhythm adjustment phenomenon and a consequence of the coupling between the individual units. In the present work, we aim to derive sufficient conditions for the synchronization of coupled Fitzhugh Nagumo Dynamics using Lyapunov stability analysis. In particular, a non-smooth Lyapunov function based upon the geodesic distance between respective states of coupled systems has been chosen as the Lyapunov function, and the concept of upper Dini-derivative has been utilized to calculate the derivative of the Lyapunov function along the error dynamics. The negative definiteness of the derivative of the Lyapunov function gives sufficient coupling gain for synchronization. The findings are verified on the Matlab simulation platform. The results should help to enhance the knowledge of neural dynamics.