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DDEBifurcationKit.jl is a component package in the BifurcationKit ecosystem. It holds the delay differential equation (DDE) utilities. While completely independent and usable on its own, users interested in using this functionality should check out BifurcationKit.jl.


Assuming that you already have Julia correctly installed, it suffices to import DDEBifurcationKit.jl in the standard way:

import Pkg; Pkg.add("https://github.com/bifurcationkit/DDEBifurcationKit.jl")

Support and citation

If you use this package for your work, we ask that you cite the following paper. Open source development as part of academic research strongly depends on this. Please also consider starring this repository if you like our work, this will help us to secure funding in the future. It is referenced on HAL-Inria as follows:

  TITLE = {{BifurcationKit.jl}},
  AUTHOR = {Veltz, Romain},
  URL = {https://hal.archives-ouvertes.fr/hal-02902346},
  INSTITUTION = {{Inria Sophia-Antipolis}},
  YEAR = {2020},
  MONTH = Jul,
  KEYWORDS = {pseudo-arclength-continuation ; periodic-orbits ; floquet ; gpu ; bifurcation-diagram ; deflation ; newton-krylov},
  PDF = {https://hal.archives-ouvertes.fr/hal-02902346/file/354c9fb0d148262405609eed2cb7927818706f1f.tar.gz},
  HAL_ID = {hal-02902346},
  HAL_VERSION = {v1},

Main features

Type of delay: Constant (C), state-dependent (SD), nested (N)

Features delay type Matrix Free Custom state Tutorial GPU
(Deflated) Krylov-Newton C/SD Yes Yes
Continuation PALC (Natural, Secant, Tangent, Polynomial) C/SD
Bifurcation / Fold / Hopf point detection C/SD Y
Fold Point continuation C/SD Y
Hopf Point continuation C/SD AbstractArray
Bogdanov-Takens Point newton C/SD Y AbstractArray
Branch point / Fold / Hopf normal form C/SD Y
Branch switching at Branch / Hopf points C/SD Y AbstractArray
Automatic bifurcation diagram computation of equilibria C/SD Y AbstractArray
Periodic Orbit (Trapezoid) Newton / continuation AbstractVector
Periodic Orbit (Collocation) Newton / continuation C/SD AbstractVector
Periodic Orbit (Parallel Poincaré / Standard Shooting) Newton / continuation AbstractArray
Fold, Neimark-Sacker, Period doubling detection AbstractVector
Continuation of Fold of periodic orbits AbstractVector
Bogdanov-Takens / Bautin / Cusp / Zero-Hopf / Hopf-Hopf point detection C/SD Y
Bogdanov-Takens / Bautin / Cusp / Zero-Hopf / Hopf-Hopf normal forms Y
Branching from Bogdanov-Takens points to Fold / Hopf curve AbstractVector