Invariant set and attractivity of nonlinear differential equations with delays
type: Item
instance of: scholarly article
title: Invariant set and attractivity of nonlinear differential equations with delays
zbMATH Open document ID: 1023.34066
DOI: 10.1016/S0893-9659(01)00138-0
author: Hongyong Zhao
author: Daoyi Xu
published in: Applied Mathematics Letters
publication date: 2003-03-10T00:00:00Z
review text: The authors discuss the invariant set, the attracting set, and the basin of attraction of nonlinear and nonautonomous delay differential equations \[ \dot y(t) =-Ay(t)+F(t,y_t)+q(t), \quad A =\text{diag} \{a_i \}. \] Such equation can be seen as a generalization of the neural network models. Some sufficient conditions are obtained for the existence of an attracting set and the basin of attraction. The approach is to employ the variation of constants formula. Two examples are given to explain the results.
reviewed by: Rong Yuan
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 1878853
zbMATH Keywords: attracting set
zbMATH Keywords: attraction basin
zbMATH Keywords: delay differential equation
zbMATH Keywords: accretive operator
zbMATH Keywords: almost-periodic function
zbMATH Keywords: semigroup
MaRDI profile type: Publication
cites work: Positively invariant sets for functional differential equations with infinite delay
cites work: Positively invariant closed sets for systems of delay-differential equations
cites work: Existence and persistence of invariant manifolds for semiflows in Banach space
cites work: Q4160745
cites work: Q5569338
cites work: Qualitative analysis of neural networks
cites work: Stability of functional differential equations
cites work: Domain of attraction of nonlinear discrete systems with delays
cites work: Integro-differential equations and delay integral inequalities
cites work: Stability in asymmetric Hopfield nets with transmission delays
cites work: Neurons with graded response have collective computational properties like those of two-state neurons.
cites work: Q4141027
cites work: Q4040931
description: scientific article; zbMATH DE number 1878853