Bifurcation properties for a sequence of approximation of delay equations
type: Item
instance of: scholarly article
title: Bifurcation properties for a sequence of approximation of delay equations
zbMATH Open document ID: 0767.34050
DOI: 10.1016/0022-247X(92)90351-D
author: Rachid Benkhalti
author: Ovide Arino
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-04-01T00:00:00Z
review text: The purpose of the paper is to investigate properties of the differential equations \(\dot x=\lambda f(x(t),\) \(x(t-1))\) and its approximation by difference equations. In section II the authors show that in any segment \([\varphi,\psi]\) of initial values (where \(\varphi<0<\psi)\) there is at least one initial value of an oscillating solution which is the limit of a sequence of initial values for the approximating equations. The results in section III contain information about bifurcation of Rabinowitz type.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 150700
zbMATH Keywords: delay differential equations
zbMATH Keywords: approximation by difference equations
zbMATH Keywords: oscillating solution
zbMATH Keywords: bifurcation of Rabinowitz type
reviewed by: George Karakostas
MaRDI profile type: Publication
cites work: Periodic solutions for: ẋ(t) = λf(x(t),x(t – 1))
cites work: Effective computation of periodic orbits and bifurcation diagrams in delay equations
cites work: A classification of the solutions of a difference equation according to their behavior at infinity
cites work: Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
cites work: A Hopf bifurcation theorem for difference equations approximating a differential equation
cites work: Periodic solutions of systems of ordinary differential equations which approximate delay equations
cites work: Some global results for nonlinear eigenvalue problems
cites work: A non-linear difference-differential equation.
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description: scientific article; zbMATH DE number 150700