Hello everyone!
I am pretty new to Julia, but I have project for which I have to analyse a bifurcation behaviour with codimension 3 for a DDE model. Hence I was wondering if BifurcationKit.jl could handle this, since in the documentation there are only example with codim 2.
Many thanks in advance!
BK does not handle codim3. The only exception is that you can continue Bogdanov Takens in 3 params but it is not shown in the tutorials. The docs mention this though
https://bifurcationkit.github.io/BifurcationKitDocs.jl/dev/codim3Continuation/
Note that codim 2 normal forms in DDE are not developped as much as for ODE in BK. They deserve a specific code that is yet to be added. I am not sure ddebitool have them, perhaps see https://scholar.google.com/scholar_url?url=https://epubs.siam.org/doi/pdf/10.1137/19M1243993&hl=en&sa=T&oi=ucasa&ct=usl&ei=7cYuZbaxDcqpy9YP6NGO-Aw&scisig=AFWwaebIfSqBkK865F_j62eFVhYQ
what codim 3 are you interested in?
I see, thank you for your quick reply! This is helpful, so it seems that I cannot use Julia for my problem. Which software would you then recommend? I see there are some recommendations in the docs but not too sure which one would be best.
what codim 3 are you interested in?
As in, what is the DDE model I am analysing, or which bifurcation am I looking for?
For DDE the most advanced is probably DDEBifTool
which bifurcation am I looking for?
yes: which bifurcation? Hopf-Hopf-Hopf?
To be honest I am not too sure… Do we have to know how it looks like prior to the analysis?
For the simpler form of the model (for which the bifurcation had codim 1) , it is a transcritical bifurcation. But for the codim 3 version, I would assume a similar behaviour.
To be more accurate, my DDE model is parameterised by 3 parameters, and I am expecting a transcritical bifurcation, where the stability of the fixed points and the location of the bifurcation depends on the 3 parameters.
Maybe I am using the wrong terminology?
Yes I think it is a wrong terminology. More or less:
codim 1 bifurcations are bifurcations which can be seen be varying a single parameter (transcritical, Hopf, pitchfork, fold)
codim 2 bifurcations are bifurcations which can be seen be varying two parameters (Hopf-Hopf, Zero-Hopf, bogdanov-takens, …)
codim 3 bifurcations are bifurcations which can be seen be varying 3 parameters
Yes indeed, sorry for using the wrong terminology. So it seems that I still can use BifurcationKit.jl then.