Analysis of Spreading Speeds with an Application to Cellular Neural Networks

TL;DR

This paper investigates the properties of spreading speeds in cellular neural networks using linear operators, providing theoretical insights and applying them to understand how templates influence propagation speeds.

Contribution

It introduces a linear operators approach to analyze spreading speeds and applies these results to cellular neural networks, highlighting the effect of templates on propagation.

Findings

Properties of spreading speeds such as sign and continuity are characterized.

Theoretical results are applied to cellular neural networks to study propagation phenomena.

Templates significantly influence the propagation speeds in CNNs.

Abstract

In this paper, we focus on some properties of the spreading speeds which can be estimated by linear operators approach, such as the sign, the continuity and a limiting case which admits no spreading phenomenon. These theoretical results are well applied to study the effect of templates on propagation speeds for cellular neural networks (CNNs), which admit three kinds of propagating phenomenon.