Synchronization control for reaction–diffusion FitzHugh–Nagumo systems with spatial sampled-data

Abstract

To gain a better understanding the synchronization mechanism of networked neurons, this paper studies the synchronization control for a class of reaction–diffusion FitzHugh–Nagumo systems, associated with a digraph containing at least one directed spanning tree. A novel control method adopting spatial sampling strategies is proposed, in which the control inputs are constructed directly on the spatial means of system state variables on sampling subsets. After discussing the existence and uniqueness of classical solutions, we show analytically that the synchronization of the controlled systems is equivalent to that of the corresponding FitzHugh–Nagumo systems under the corresponding control inputs. Based on the study on general algebraic connectivity, a sufficient condition for the system synchronization is given, together with case simulations to illustrate the effectiveness and potential of the new control method.