Uniform approximation of impulsive Hopfield cellular neural networks by piecewise constant arguments on \([\tau,\infty)\)
type: Item
instance of: scholarly article
title: Uniform approximation of impulsive Hopfield cellular neural networks by piecewise constant arguments on \([\tau,\infty)\)
zbMATH Open document ID: 1492.34083
author: Yanyan Li
published in: Acta Applicandae Mathematicae
publication date: 2021-05-19T00:00:00Z
review text: The paper deals with an approximation on a semi-axes \([t_0,\infty)\) the following non-linear impulsive system \[ y'_i(t)=-a_i(t)y_i(t)+\sum_{j=1}^m b_{ij}(t)f_j(y_j(t))+c_i(t),~~t\neq t_k, \]\[ \Delta y_i(t_k)=-q_{i,k}y_i(t_k^-)+e_{i,k}+I_{i,k}(y_i(t_k^-)),~~t=t_k, ~ y_i(t_0)=y_i^0 \] by the system \[ z'_i(t)=-a_i(t)z_i(t)+\sum_{j=1}^m b_{ij}(t)f_j(z_j(\gamma(t)))+c_i(t),~~t\neq \gamma (t_k), \]\[ \Delta z_i(\gamma (t_k))=-q_{i,k}z_i(\gamma (t_k)^-)+e_{i,k}+I_{i,k}(z_i(\gamma (t_k)^-)),~~t=\gamma (t_k), ~ z_i(t_0)=z_i^0, \] where \(\gamma(t)\) a piecewise constant argument.
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 34K07
zbMATH DE Number: 7349874
zbMATH Keywords: piecewise constant arguments
zbMATH Keywords: hybrid equations
zbMATH Keywords: Gronwall's inequality
zbMATH Keywords: approximation of solutions
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: cellular neural networks
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
full work available at URL: s10440-020-00373-3
OpenAlex ID: W3112810987
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DOI: 10.1007/S10440-020-00373-3
description: scientific article; zbMATH DE number 7349874