article

Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL

Authors:

K. Engelborghs,

D. RooseAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 28, Issue 1

Pages 1 - 21

https://doi.org/10.1145/513001.513002

Published: 01 March 2002 Publication History

Abstract

We describe DDE-BIFTOOL, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.

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Index Terms

Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
1. Mathematics of computing
  1. Mathematical analysis
  2. Mathematical software
2. Theory of computation
  1. Design and analysis of algorithms

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 28, Issue 1

March 2002

131 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/513001

Issue’s Table of Contents

Copyright © 2002 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 2002

Published in TOMS Volume 28, Issue 1

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Liu QZhang X(2024)Chaos detection in predator-prey dynamics with delayed interactions and Ivlev-type functional responseAIMS Mathematics10.3934/math.202411969:9(24555-24575)Online publication date: 2024
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Chen-Charpentier B(2024)A Model of Hepatitis B Viral Dynamics with DelaysAppliedMath10.3390/appliedmath40100094:1(182-196)Online publication date: 1-Feb-2024
https://doi.org/10.3390/appliedmath4010009
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