Exponential synchronization of 2D cellular neural networks with boundary feedback

Abstract

In this work we propose a new mathematical model of 2D cellular neural networks (CNN) in terms of the lattice FitzHugh-Nagumo equations with boundary feedback. The model features discrete Laplacian operators and periodic boundary feedback instead of the interior-clamped or mean-field feedback. We first prove the globally dissipative dynamics of the solutions through a priori uniform estimates. In the main result we show that the 2D cellular neural networks are exponentially synchronized if the computable threshold condition is satisfied by the synaptic gap signals of pairwise boundary cells of the grid and the system parameters with a linear feedback coupling coefficient tunable in applications.

Keywords:

• Cellular neural network
• lattice FitzHugh-Nagumo equations
• exponential synchronization
• boundary feedback
• dissipative dynamics

2010 Mathematics Subject Classification;:

• 34A33
• 34D06
• 37B15
• 37L60
• 92B20

Disclosure statement

No potential conflict of interest was reported by the authors.