I am writing this post to report about my package BifurcationKit.jl.
The focus of this 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 using a new technics called deflated continuation. Combined with automatic Bifurcation Diagram (BD) of my previous post, its offers a new way of obtaining a bifurcation diagram for PDE (or nonlocal equations,…) albeit allowing to discovering disconnected branches. A simple example is shown here.
I have several improvements to the basic underlying algo (not yet pushed) but I am not sure how to parallelize it. If you want to take a look at it, it is located here.
WIth this is new very exciting method, BifurcationKit.jl offers 2 powerful ways of computing BD automatically, each one with its own pro and cons.