Adaptive synchronization control of coupled chaotic neurons in the external electrical stimulation

In this paper we present a combined algorithm for the synchronization control of two gap junction coupled chaotic FitzHugh-Nagumo (FHN) neurons in the external electrical stimulation. The controller consists of a combination of dynamical sliding mode control and adaptive backstepping control. The combined algorithm yields an adaptive dynamical sliding mode control law which has advantages over static sliding mode-based controller of chattering-free, i.e., a sufficiently smooth control input signal is generated. It is shown that the proposed control scheme can not only compensate for the system uncertainty, but also guarantee the stability of the synchronized error system. In addition, numerical simulations are also performed to demonstrate the effectiveness of the proposed adaptive controller.