Robust adaptive sliding mode control for synchronization of space-clamped FitzHugh–Nagumo neurons

Unlike taking the same external electrical stimulation to discuss chaotic synchronization in the literature, the synchronization between two uncouple FitzHugh–Nagumo (FHN) neurons with different ionic currents and external electrical stimulations is considered. The main contribution of this study is the application of a robust adaptive sliding-mode controller instead of the active elimination. The proposed sliding mode controller associated with time varying feedback gains cannot only tackle the system uncertainties and external disturbances, but also compensate for the mismatch nonlinear dynamics of synchronized error system without direct cancellation. Meanwhile, these feedback gains are not determined in advance but updated by the adaptive laws. Sufficient conditions to guarantee the stable synchronization are given in the sense of the Lyapunov stability theorem. In addition, numerical simulations are also performed to verify the effectiveness of presented scheme.