Exponential Synchronization of 2D Cellular Neural Networks with Boundary Feedback

TL;DR

This paper introduces a new 2D cellular neural network model with boundary feedback, establishing conditions for exponential synchronization based on network parameters, with potential for extension to higher dimensions.

Contribution

It proposes a novel 2D CNN model with boundary feedback and derives a threshold condition for exponential synchronization, advancing the understanding of neural network dynamics.

Findings

Threshold condition for synchronization derived

Synchronization depends on boundary gap signals and structural parameters

Method applicable to higher-dimensional neural networks

Abstract

In this work we propose a new model of 2D cellular neural networks (CNN) in terms of the lattice FitzHugh-Nagumo equations with boundary feedback and prove a threshold condition for the exponential synchronization of the entire neural network through the \emph{a priori} uniform estimates of solutions and the analysis of dissipative dynamics. The threshold to be satisfied by the gap signals between pairwise boundary cells of the network is expressed by the structural parameters and adjustable. The new result and method of this paper can also be generalized to 3D and higher dimensional FitzHugh-Nagumo type or Hindmarsh-Rose type cellular neural networks.