Synchronization of a set of coupled chaotic FitzHugh-Nagumo and Hindmarsh-Rose neurons with external electrical stimulation

This paper addresses problem of synchronization of n-neurons which are electrically coupled to each other. Gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons and linearly coupled Hindmarsh-Rose (H-R) neurons are considered with each neuron subjected to external electrical stimulation. The neurons are assumed to be linked in a chain-like structure. It is shown that the suitable choice of coupling strength of gap junction is sufficient to meet out the synchronization condition. Simple stability analysis based on partial contraction approach is used to establish the exponential convergence of states of different neurons to each other. The conditions for complete synchronization are derived analytically for a general system having n-electrically coupled neurons. The advantage of the proposed approach lies in its simplicity and provides an alternative method of achieving synchronization. Further, in comparison with Lyapunov-based analysis, the formulation of error dynamics is avoided while establishing synchronizing conditions. Numerical simulations are shown for both FHN and Hindmarsh-Rose neurons separately to justify the effectiveness of the proposed approach to meet out synchronization requirements.