Rigorous verification of Hopf bifurcations in functional differential equations of mixed type
type: Item
instance of: scholarly article
title: Rigorous verification of Hopf bifurcations in functional differential equations of mixed type
zbMATH Open document ID: 1496.34103
author: Kevin E. M. Church
author: Jean-Philippe Lessard
published in: Physica D
publication date: 2022-02-22T00:00:00Z
review text: The paper is concerned with the development of a numerical method to prove the existence of Hopf bifurcations in simple functional differential equations of mixed type, otherwise known as advance-delay equations, or sometimes as forward-backward equations. The question of interest is to consider the properties of the eigenvalues, and use is made of the Newton-Kantorovich theorem. The authors prove the existence of Hopf bifurcations in the Lasota-Wazewska-Czyzewska model and the existence of periodic traveling waves in the Fisher equation with nonlocal reaction. The overall objective of the work is to `develop numerical methods which can lead to computer-assisted proofs of existence of different type of dynamical objects arising in the study of differential equations.' Consequently, there is a section that discusses computer-assisted proofs of some of the theorems presented and links are provided to the relevant code.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K21
Mathematics Subject Classification ID: 37M20
zbMATH DE Number: 7479416
zbMATH Keywords: functional differential equation
zbMATH Keywords: mixed type
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: rigorous numerics
zbMATH Keywords: periodic traveling wave
Wikidata QID: Q115341678
reviewed by: Neville J. Ford
describes a project that uses: Knut
describes a project that uses: MATCONT
describes a project that uses: DDE-BIFTOOL
describes a project that uses: GitHub
MaRDI profile type: Publication
full work available at URL: j.physd.2021.133072
OpenAlex ID: W3208706555
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Rigorous verification of Hopf bifurcations in functional differential equations of mixed type (DOI)
DOI: 10.1016/J.PHYSD.2021.133072