a Matlab package for bifurcation
of delay differential equations
Tatyana Luzyanina, Giovanni Samaey,
Dirk Roose, Koen Verheyden
K.U.Leuven, Department of Computer Science
DDE-BIFTOOL is a Matlab package for numerical bifurcation and stability
delay differential equations with several fixed discrete and/or state-dependent delays.
It allows the computation, continuation and stability analysis of
steady state solutions, their Hopf and fold bifurcations, periodic
solutions and connecting orbits (but the latter only for the constant delay
case). Stability analysis of steady state solutions is achieved
through computing approximations and corrections to the rightmost
characteristic roots. Periodic solutions, their Floquet multipliers and connecting
are computed using piecewise polynomial collocation on adaptively refined
- Text material:
The package and its use are described in the manual
 (and the addendum ).
The paper  includes additional examples and comments.
A brief description of the numerical methods used and additional references are included in
[1,2,3]. All implemented methods are described in detail in the
The package is freely available for scientific use.
It is a typical research code which comes with no guarantee whatsoever.
Before obtaining the package, download and read the manual
(and the addendum ) to see whether the package suits your needs. If so, proceed to the warranty notice and download page.
Important notice: users of DDE-BIFTOOL are
assumed to have a basic knowledge on bifurcation analysis
of dynamical systems and on the nature of delay equations.
The manual on the package does not replace the corresponding text books!
- Common questions and mistakes:
for comments to common questions and mistakes.
T.Luzyanina, G. Samaey, DDE-BIFTOOL v. 2.00: a Matlab package for bifurcation analysis
of delay differential equations, Technical Report TW-330,
Department of Computer Science, K.U.Leuven, Leuven, Belgium, 2001.
 K. Engelborghs, T. Luzyanina & D. Roose, Numerical bifurcation analysis
of delay differential equations using DDE-BIFTOOL,
ACM Transactions on Mathematical Software, Vol. 28, Number 1, p. 1-21, 2002.
 K. Verheyden, New functionality in DDE-BIFTOOL v. 2.03. Addendum to the manual of DDE-BIFTOOL v. 2.00 (and v. 2.02), unpublished, March 2007.
Related information on delay equations
- Publications on delay equations:
For a list of publications on delay equations of the Scientific Computing
Research Group, K.U.Leuven, in the period 1996 - 2004,
Links to publically available software packages
for delay equations (time integration, bifurcation analysis, control
design, parameter estimation)
Comments, suggestions and questions can
This page, http://www.cs.kuleuven.ac.be/cwis/research/twr/research/software/delay/ddebiftool.shtml, is
Last modified March 15, 2007.