Adaptive synchronization for nonlinear FitzHugh-Nagumo neurons in external electrical stimulation

This paper investigates the synchronization problem for FitzHugh-Nagumo (FHN) neurons in external electrical stimulations. Using the sliding mode control technique, an adaptive control law is established that guarantees synchronization even when the parameters of the master and slave FHN neurons are fully unknown. A proportional-integral switching surface is introduced to simplify the task of assigning the stability of the closed-loop error system in the sliding mode. Furthermore, the proposed synchronization scheme is then applied to a secure communication system. Computer simulations are provided to verify the effectiveness of the proposed adaptive synchronization scheme.