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DDEBifurcationKit

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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.

Installation

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:

@misc{veltz:hal-02902346,
  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)

Featuresdelay typeMatrix FreeCustom stateTutorialGPU
(Deflated) Krylov-NewtonC/SDYesYes
Continuation PALC (Natural, Secant, Tangent, Polynomial)C/SD
Bifurcation / Fold / Hopf point detectionC/SDY
Fold Point continuationC/SDY
Hopf Point continuationC/SDAbstractArray
Bogdanov-Takens Point newtonC/SDYAbstractArray
Branch point / Fold / Hopf normal formC/SDY
Branch switching at Branch / Hopf pointsC/SDYAbstractArray
<span style="color:red">Automatic bifurcation diagram computation of equilibria</span>C/SDYAbstractArray
Periodic Orbit (Trapezoid) Newton / continuationAbstractVector
Periodic Orbit (Collocation) Newton / continuationC/SDAbstractVector
Periodic Orbit (Parallel Poincaré / Standard Shooting) Newton / continuationAbstractArray
Fold, Neimark-Sacker, Period doubling detectionAbstractVector
Continuation of Fold of periodic orbitsAbstractVector
Bogdanov-Takens / Bautin / Cusp / Zero-Hopf / Hopf-Hopf point detectionC/SDY
Bogdanov-Takens / Bautin / Cusp / Zero-Hopf / Hopf-Hopf normal formsY
Branching from Bogdanov-Takens points to Fold / Hopf curveAbstractVector