Geometric methods of global attraction in systems of delay differential equations
type: Item
instance of: scholarly article
title: Geometric methods of global attraction in systems of delay differential equations
zbMATH Open document ID: 1412.34217
author: Hassan A. El-Morshedy
author: Alfonso Ruiz-Herrera
published in: Journal of Differential Equations
publication date: 2018-10-02T00:00:00Z
review text: A geometric method is derived to deduce delay-independent and delay-dependent criteria of global attraction to a non-trivial equilibrium in a class of systems of delay differential equations. The results are expressed in terms of some dynamical properties of a suitable scalar discrete equation. An advantage of the approach is that delay-dependent criteria can be obtained. Two well known models where the approach provides new information are presented.
reviewed by: Ioannis P. Stavroulakis
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K21
zbMATH DE Number: 6946035
zbMATH Keywords: dominance
zbMATH Keywords: delay dependent criteria
zbMATH Keywords: Nicholson's blowfly equation
zbMATH Keywords: global attraction
MaRDI profile type: Publication
full work available at URL: j.jde.2017.07.001
OpenAlex ID: W2734642455
cites work: Bifurcations in delay differential equations and applications to tumor and immune system interaction models
cites work: General model of a cascade of reactions with time delays: global stability analysis
cites work: Q5847520
cites work: Global attractivity in a population model with nonlinear death rate and distributed delays
cites work: Global attractors for difference equations dominated by one-dimensional maps
cites work: Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays
cites work: Persistence, permanence and global stability for an \(n\)-dimensional Nicholson system
cites work: To connect or not to connect isolated patches
cites work: An Advection and Age-Structured Approach to Modeling Bird Migration and Indirect Transmission of Avian Influenza
cites work: Slowing the evolution of insecticide resistance in mosquitoes: a mathematical model
cites work: A Mathematical Model for the Control and Eradication of a Wood Boring Beetle Infestation
cites work: Q4261342
cites work: Epidemic spread and variation of peak times in connected regions due to travel-related infections -- dynamics of an antigravity-type delay differential model
cites work: A degenerate Hopf bifurcation in retarded functional differential equations, and applications to endemic bubbles
cites work: Global stability of a class of delay differential systems
cites work: On the global attractor of delay differential equations with unimodal feedback
cites work: Attractivity, multistability, and bifurcation in delayed Hopfield's model with non-monotonic feedback
cites work: Delayed population models with Allee effects and exploitation
cites work: Addendum to: ``Attractivity, multistability, and bifurcation in delayed Hopfield's model with non-monotonic feedback''
cites work: Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
cites work: Using Lyapunov Functions to Construct Lyapunov Functionals for Delay Differential Equations
cites work: Analysis of dispersal effects in metapopulation models
cites work: Stability switches, Hopf bifurcations, and spatio-temporal patterns in a delayed neural model with bidirectional coupling
cites work: Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain
cites work: Map dynamics versus dynamics of associated delay reaction–diffusion equations with a Neumann condition
DOI: 10.1016/J.JDE.2017.07.001
description: scientific article; zbMATH DE number 6946035