Feedback Synchronization of FHN Cellular Neural Networks

Abstract

In this work we study the synchronization of ring-structured cellular neural networks modeled by the lattice FitzHugh-Nagumo equations with boundary feedback. Through the uniform estimates of solutions and the analysis of dissipative dynamics, the synchronization of this type neural networks is proved under the condition that the boundary gap signal exceeds the adjustable threshold.

Exponential Synchronization of 2D Cellular Neural Networks with Boundary Feedback

“…This work aims to prove the exponential synchronization of the 2D FitzHugh-Nagumo cellular neural networks with the new feature of the boundary feedback, which is a substantial generalization of feedback synchronization for one-dimensional FitzHugh-Nagumo cellular neural networks [28] shown by the authors. In this CNN model, the cell template with the synapsis is described by the discrete version of the 2D partly diffusive FitzHugh-Nagumo equations with boundary feedback control.…”

“…Recently the authors proved results on the exponential synchronization for the boundary coupled Hindmarsh-Rose neuron networks in [23,24], the boundary coupled partly diffusive FitzHugh-Nagumo neural networks in [27], and the feedback synchronization of the one-dimensional FitzHugh-Nagumo CNN in [28].…”