Synchronization of coupled chaotic neurons with unknown time delays via adaptive backstepping control

In this study, an adaptive Neural Network (NN) based backstepping controller is proposed to realize chaos synchronization of two gap junction coupled FitzHugh-Nagumo (FHN) neurons with uncertain time delays. In the designed backstepping controller, a simple Radial Basis Function (RBF) NN is used to approximate the uncertain nonlinear part of the error dynamical system. The weights of the NN are tuned on-line. A Lyapunov-Krasovskii function is designed to overcome the difficulties from the unknown time delays. Moreover, to relax the requirement for boundness of disturbance, an adaptive law to adapt the disturbance in real time is given. According to the Lyapunov stability theory, the stability of the closed error system is guaranteed. The control scheme is robust to the uncertainties such as approximate error, ionic channel noise and external disturbances. Chaos synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.