I'm a physics graduate student. My interests are mainly statistical physics, so I usually deal with non-linear systems (both deterministic and stochastic). I did a dynamical system course, where we mainly studied the Strogatz's Non-linear Dynamics and Chaos, as well as some selected advanced topics.
So I believe that my bifurcation theory skills are OK for usual systems, but, from time to time, I encounter problems. For example, systems with bifurcations of codimension larger than 1, homoclinic bifurcations, or having to analyse bifurcations in a PDE (usually the Fokker-Planck equation). In my research it is very important to classify all bifurcation lines and points, and when these difficulties arise I really struggle to find a solution. I also tried to use AUTO-07p but at the end I'm not able to get good results from the software.
Long story short, I think I need to upgrade my tools in bifurcation theory. I tried to read Kuznetsov's Elements of Applied Bifurcation Theory, but it is written in a language that is difficult to understand for me. The book seems excellent, specially the last part about numerical methods, but for the moment is not very accesible.
I have been reading some questions about source recommendations here but they do not seem very appealing (at least, at first sight).
Do you know a book (or course, or review...) on bifurcation theory, focused in practice, which is easy to read / amenable for physicist? I would need it to cover higher codimension bifurcations and homoclinic bifs. (At least, something I can use to understand better some concepts and then jump to Kuznetsov).
Do you have any source on how to use AUTO-07p, besides from official docs? I'm pretty sure the program is super-useful but I'm not using it properly. I would be very interested in solved exercises with it.
This is less important, but also something about bifurcation analysis in PDEs (spatiotemporal pattern formation) or analysis of bifurcations when stochastic noise is present would be excellent.
Thank you very much in advance!
