Robust adaptive synchronization of uncoupled FitzHugh-Nagumo neurons under disturbances and uncertain external electric stimulation

This paper describes a nonlinear robust adaptive control for synchronization of uncoupled FitzHugh-Nagumo (FHN) neurons with uncertainty in the amplitude of stimulation current and under disturbances. First, we propose an adaptive nonlinear control for asymptotic synchronization of neurons under the uncertain amplitude of stimulation current. Then, we modify the adaptive control law to deal with bounded disturbances. Proposed robust adaptive control law ensures uniformly ultimately bounded synchronization error under uncertain stimulation and disturbances. The results of the proposed methodologies are verified through numerical simulations.