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December  2009, 2(4): 931-965. doi: 10.3934/dcdss.2009.2.931

A survey of some results on overstability and bifurcation delay

Augustin Fruchard 1, and  Reinhard Schäfke 2,

1. 

Laboratoire de Mathématiques, Informatique et Applications, Faculté des Sciences et Techniques, Université de Haute Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse cedex, France
2. 

Institut de Recherche Mathématique Avancée, U.F.R. de Mathématiques et Informatique, Université de Strasbourg et C.N.R.S., 7, rue René Descartes, F-67084 Strasbourg cedex, France

Received  September 2008 Revised  April 2009 Published  September 2009

We give a non-exhaustive overview of the problem of bifurcation delay from its appearance in France at the end of the eighties to the most recent contributions. We present the bifurcation delay for differential equations as well as for discrete dynamical systems.
Keywords: singular perturbation., canard solution, Bifurcation delay, Poincaré-Andronov-Hopf bifurcation, dynamic bifurcation.
Mathematics Subject Classification: Primary: 34E15, 39A; Secondary: 03.
Citation: Augustin Fruchard, Reinhard Schäfke. A survey of some results on overstability and bifurcation delay. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : 931-965. doi: 10.3934/dcdss.2009.2.931
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