Synchronization of two uncoupled Fitzhugh-Nagumo neurons via nonlinear control

Individual neurons can exhibit irregular behavior, whereas ensembles of different neurons might synchronize in order to process biological information or to produce regular, rhythmical activity. Therefore, the study of synchronization processes for populations of interacting neurons is basic to the understanding of some key issues in neuroscience. In the present study, we first investigated dynamic behaviors of FitzHugh-Nagumo (FHN) neurons stimulated by external electrical signal. Second, we formulated a new method for synchronization of two uncoupled FHN neurons. By using a Lyapunov function, a nonlinear control law is designed that guarantees that two neurons are synchronized even when the external electrical stimulations applied to each neuron are different. Finally, in order to verify the effectiveness of the proposed method, numerical simulations were performed, the results of which are provided herein.