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Singularly Perturbed Dynamical Systems


Singularly perturbed systems are ubiquitous in mathematics and its applications. These problems often appear due to a time scale
separation i.e. when two processes evolve at substantially different rates. The goal of this project is to advance the theory of multiple time
scale systems in the following directions.
(1) Mixed-mode oscillations: These complicated oscillatory patterns appear in a wide range of models. In particular, high-dimensional
problems are of interest.
(2) Multiparameter problems: Bifurcation theory of mulitscale systems, particularly for two or more singular parameters, has to be
developed. A starting point are two-parameter bifurcation curves in the FitzHugh-Nagumo equation.
(3) Geometric de-singularization: Extension and development of the so-called blow-up method are a major part of this project.
(4) Extension of current methods: A further driving question will be how the theory for finite-dimensional systems extends to stochastic and
partial differential equations; even the understanding of simple examples is anticipated to very interesting.

Call for proposal

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Karlsplatz 13
1040 Wien
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 75 000
Administrative Contact
Peter Szmolyan (Prof.)