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DDEBifurcationKit
Documentation | Build Status | Downloads |
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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)
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 | |||
C/SD | Y | AbstractArray | |||
Branch point / Fold / Hopf normal form | C/SD | Y | |||
Branch switching at Branch / Hopf points | C/SD | Y | AbstractArray | ||
<span style="color:red">Automatic bifurcation diagram computation of equilibria</span> | C/SD | Y | AbstractArray | ||
AbstractVector | |||||
Periodic Orbit (Collocation) Newton / continuation | C/SD | AbstractVector | |||
AbstractArray | |||||
AbstractVector | |||||
AbstractVector | |||||
Bogdanov-Takens / Bautin / Cusp / Zero-Hopf / Hopf-Hopf point detection | C/SD | Y | |||
Y | |||||
AbstractVector |