Global synchronization of N neurons in external electrical stimulation via active control

In this paper, active control law is derived and applied to control and synchronize N(N ≥ 3) unidirectional coupled Fitzhugh-Nagumo neurons in external electrical stimulation. Firstly, the dynamical behavior of the nonlinear Fitzhugh-Nagumo model responding to various external electrical stimulations is studied. Then, using the results of the analysis, the active control strategy is designed for global synchronization of the N(N ≥ 3) unidirectional coupled neurons and stabilizing the chaotic trajectory of the slave system to desired periodic orbit of the master system. Numerical simulations demonstrate the validity and feasibility of the proposed method.