Geometric Desingularization of Higher Codimension Singularities in Fast-Slow Systems
Final Report Abstract
The general framework of the project was set in the area of systems with multiple time scales. These dynamical systems appear in virtually all applications for complex systems as generally different biological, chemical and physical processes tend to have widely differing rates at which they evolve. One major challenge in this area is the dynamical complexity of possible behaviors such systems can exhibit. In particular, if the number of variables in the system increases, we are still very far away from understanding the required mathematics to really study them rigorously. The project contributed to this research avenue by considering generalizations to higher-dimensional singularities that arise mainly in energy-driven (or gradient) systems. Furthermore, we have tackled the first steps to transfer the low-dimensional mathematical methods to the area of complex networks. Our results show that several low-dimensional results generalize in quite surprising ways to higher-dimensional settings.
Publications
-
On network dynamical systems with a nilpotent singularity
Jardón-Kojakhmetov, Hildeberto & Kuehn, Christian
-
Persistent Synchronization of Heterogeneous Networks with Time-Dependent Linear Diffusive Coupling. SIAM Journal on Applied Dynamical Systems, 23(2), 1540-1578.
Jardón-Kojakhmetov, Hildeberto; Kuehn, Christian & Longo, Iacopo P.
-
The hyperbolic umbilic singularity in fast-slow systems. Nonlinearity, 37(9), 095036.
Jardón-Kojakhmetov, Hildeberto; Kuehn, Christian & Steinert, Maximilian
-
Fast-Moving Pattern Interfaces Close to a Turing Instability in an Asymptotic Model for the Three-Dimensional Bénard–Marangoni Problem. Journal of Nonlinear Science, 35(5).
Hilder, Bastian & Jansen, Jonas
