Singularly Perturbed Dynamical Systems

05.07.2011 - 01.09.2015
Research funding project
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 multiscale 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 point 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.

People

Project leader

Project personnel

Institute

Grant funds

  • European Commission (EU) FP7 III. PEOPLE (Marie Curie Actions) 7.Rahmenprogramm für Forschung European Commission - Framework Programme European Commission Call identifier FP7-PEOPLE-2010-RG Application number 271086

Research focus

  • Mathematical and Algorithmic Foundations: 100%

Publications