Affiliation:
1. Katholieke Universiteit Leuven, Belgium
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Reference29 articles.
1. Ascher U. M. Mattheij R. M. M. and Russell R. D. 1988. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Prentice Hall. Ascher U. M. Mattheij R. M. M. and Russell R. D. 1988. Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Prentice Hall.
2. Periodic Solutions in a Model of Recurrent Neural Feedback
3. DKLAG6: a code based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent functional differential equations
4. Doedel E. J. Champneys A. R. Fairgrieve T. F. Kuznetsov Y. A. Sandstede B. and Wang X. 1997. AUTO97: Continuation and bifurcation software for ordinary differential equations; available via ftp.cs.concordia.ca in directory pub/doedel/auto. Doedel E. J. Champneys A. R. Fairgrieve T. F. Kuznetsov Y. A. Sandstede B. and Wang X. 1997. AUTO97: Continuation and bifurcation software for ordinary differential equations; available via ftp.cs.concordia.ca in directory pub/doedel/auto.
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