Neural adaptive synchronization control of chaotic FitzHugh-Nagumo neurons in the external electrical stimulation

This paper presents a neural adaptive control strategy for the chaotic synchronization of two electrically coupled FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. The control scheme integrates the sliding mode control, input-output linearization technique, and neural network approximation. Through input-output linearization, a sliding mode controller is derived firstly to compensate the nonlinearity of the coupled neuronal system. Considering the nonlinearity of neural system is usually unknown in practical applications, an adaptive sliding mode control law is designed with a radial basis function (RBF) neural network to approximate the unknown system nonlinearity. The neural network parameters are updated according to the Lyapunov approach. It is shown that using the proposed control approach, chaos synchronization between two coupled neurons can be obtained. Simulation results demonstrate the effectiveness of the proposed control scheme.