December  2009, 2(4): i-iii. doi: 10.3934/dcdss.2009.2.4i

Preface

1. 

Hasselt University, Campus Diepenbeek, Agoralaan-Gebouw D, B-3590 Diepenbeek, Belgium

2. 

Universiteit Hasselt, Campus Diepenbeek, Agoralaan–gebouw D, 3590 Diepenbeek

3. 

Department of Mathematics and Statistics, University of Sydney, Sydney

Published  September 2009

The theory of slow-fast systems is a challenging field both from the viewpoint of theory and applications. Advances made over the last decade led to remarkable new insights and we therefore decided that it is worthwhile to gather snapshots of results and achievements in this field through invited experts. We believe that this volume of DCDS-S contains a varied and interesting overview of different aspects of slow-fast systems with emphasis on 'bifurcation delay' phenomena. Unfortunately, as could be expected, not all invitees were able to sent a contribution due to their loaded agenda, or the strict deadlines we had to impose.
   Slow-fast systems deal with problems and models in which different (time- or space-) scales play an important role. From a dynamical systems point of view we can think of studying dynamics expressed by differential equations in the presence of curves, surfaces or more general varieties of singularities. Such sets of singularities are said to be critical. Perturbing such equations by adding an $\varepsilon$-small movement that destroys most of the singularities can create complex dynamics. These perturbation problems are also called singular perturbations and can often be presented as differential equations in which the highest order derivatives are multiplied by a parameter $\varepsilon$, reducing the order of the equation when $\varepsilon\to 0$.

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Citation: P. De Maesschalck, Freddy Dumortier, Martin Wechselberger. Preface. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : i-iii. doi: 10.3934/dcdss.2009.2.4i
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