2026-08-13 –, Tent — RW1
Bifurcation theory studies dynamical systems as functions of parameters and detects qualitative changes in their dynamical regimes. bifurcationkit is the main Julia organization dedicated to the numerical analysis of bifurcations in general dynamical systems, and it has been under steady development for over six years. In this talk, I will present recent improvements to the algorithms and API, and showcase high-performance applications.
For the core package BifurcationKit, little has changed on the surface, although substantial modifications have been made under the hood.
First, the computation of branches emanating from bifurcation points has been significantly improved. Surprisingly, despite the success of the automatic branching procedure (see the figure), the underlying procedure was in fact numerical unstable. Fixing this issue has further strengthened the branching capabilities of BifurcationKit, which I will illustrate.
Second, closures have been removed from most parts of the code related to the computation of periodic orbits and the continuation of bifurcation points of equilibria and periodic orbits. This has considerably simplified the implementation and led to a new (breaking) API, which I will present. I will demonstrate these enhancements.
Finally, I will report recent advances in the computation of bifurcations of periodic orbits in delay differential equations (which are ubiquitous in biology), an area for which little package currently exists in the Julia ecosystem. I will present examples in both small and moderately large dimensions.
My research is axed on descriptions and analysis of neural networks from the point of view of dynamical systems. My goal is to develop numerical / theoretical tools that allow an efficient study of these systems in order to draw predictions to be tested in experiments in neurobiology.