Propagation phenomena for CNNs with asymmetric templates and distributed delays
type: Item
instance of: scholarly article
title: Propagation phenomena for CNNs with asymmetric templates and distributed delays
zbMATH Open document ID: 1406.35443
author: Xiao-Qiang Zhao
author: Zhixian Yu
published in: Discrete and Continuous Dynamical Systems
publication date: 2017-11-14T00:00:00Z
review text: This work considers a Cellular Neural Network modeled by a sequence of nodes, each of which has a voltage varying in time according to the interaction with the neighbors (up to a certain level). Such an interaction, described by a nonlinear term, can be asymmetric and exhibits distributed time delay. When the nonlinearity is nondecreasing, the theory of monotone dynamical systems is applied to prove the existence and some estimates of asymptotic speed of spread, both to the left and to the right. When the nonlinearity is not monotone, instead, the same results are obtained by comparing the original system with two monotone ones and using the previous part. In addition, the authors show that the spreading speed coincides with the minimal speed of traveling waves. Finally, some numerical experiments are presented.
reviewed by: Andrea Tellini
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6806973
zbMATH Keywords: spreading speeds
zbMATH Keywords: travelling waves
zbMATH Keywords: monotone semiflows
zbMATH Keywords: cellular neural networks (CNNs)
zbMATH Keywords: non-monotone
MaRDI profile type: Publication
full work available at URL: dcds.2018039
OpenAlex ID: W2765182962
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DOI: 10.3934/DCDS.2018039
description: scientific article; zbMATH DE number 6806973