Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons with Single-and Dual-State Gap Junctions under Ionic Gates and External Electrical Disturbance

Abstract

Synchronization plays an essential role in processing information and decisions by neurons and their networks in the brain, and it is useful to study the synchronization of neuron networks, as a part of the process of understanding the functionality of both healthy and diseased brains. In the past, most studies had developed control schemes relating to synchronization problems which were limited to two or three neurons, which cannot depict the dynamic synchronization behavior of neuron networks. In this paper, we investigated the synchronization issues associated with a ring-structured network of FitzHugh-Nagumo (FHN) neurons, under external electrical stimulation, and with single- and dual-state gap junctions. In addition, the gap junctions (coupling)s and ionic gate disturbances were included in the dynamics of this FHN neuronal network, making our work both more realistic, and more challenging. Thus, each neuron in this network was influenced synaptically by its neighboring two neurons. A simple, robust, and adaptive control scheme, for both a single- and the dual-gap-junction network has been proposed, which will compensate for the nonlinear dynamics without direct cancelation to achieve synchronization. Sufficient conditions to guarantee synchronization of both membrane potentials and recovery variables were derived by using Lyapunov stability theory. Finally, the proposed scheme was validated, and its efficacy was comprehensively analyzed through numerical simulations.