BifurcationKit.jl: Automatic Bifurcation Diagrams in Julia

Dear All,

I am writing this post to report about my package BifurcationKit.jl. First, this is a new name for an old package :wink:

The focus of this new version is automatic bifurcation diagram (aBD) computation for PDEs. Although this is a bit preliminary, I am excited to share some advances regarding the case of equilibria (see figure below which shows the equilibria of a PDE as function of a parameter (x-axis)).

Notably, the algorithm (aBD) is quite short, what it requires is a robust branch switching algorithm. As you can tell, computing this diagram manually (by telling which branch point to consider) will be quite time consuming and that’s why you usually find partial version of this in the litterature.

There aren’t so many softwares which allow to do this, and even less for PDE or large scale problems (I know one which is not open source nor released). For now, the aBD works for simple branch points but I will soon commit a version which works even when the PDE/functional has symmetries (see teaser). With this, the package would definitely be beyond state of the art…

You can find a basic example and a more involved one for a 1d PDE.

Hopefully, some of you will find this useful,