Local dynamics of an equation with a large state-dependent delay
type: Item
instance of: scholarly article
title: Local dynamics of an equation with a large state-dependent delay
zbMATH Open document ID: 1384.34081
DOI: 10.1134/S1064562415050221
author: I. S. Kashchenko
author: S. A. Kashchenko
published in: Doklady Mathematics
publication date: 2016-01-29T00:00:00Z
review text: In this paper, the authors deal with two differential equations with a large density dependent delay. The first equation is a first order scalar DDE and the second is a second order DDE with a damping term. They analyze the behaviors of solutions to these two equations in a neighborhood of an equilibrium by explore the stability of the equilibrium, which is related to the global dynamics of a nonlinear parabolic equation with periodic or anti-periodic boundary solutions which is known as a quasi-normal form. Asymptotic formulas are presented that relate the solutions of the quasi-normal form and the original equation.
reviewed by: Xingfu Zou
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34K21
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 6537034
zbMATH Keywords: delay differential equation
zbMATH Keywords: state dependent delay
zbMATH Keywords: parabolic equation
zbMATH Keywords: quasi-normal form
zbMATH Keywords: asymptotic formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6537034