Characterizing Slow Exit and Entrance Points

Details Characterizing Slow Exit and Entrance Points Characterizing Slow Exit and Entrance Points

2012-01-29

arxiv.org/abs/1201.6083v2

Electronic Journal of Differential Equations, Vol. 2010, No. 106, pp. 1-20, 2010

Mathematics

Dynamical Systems

preprint version - for final version see journal reference

Scientific paper

Geometric Singular Perturbation Theory (GSPT) and Conley Index Theory are two powerful techniques to analyze dynamical systems. Conley already realized that using his index is easier for singular perturbation problems. In this paper, we will revisit Conley's results and prove that the GSPT technique of Fenichel Normal Form can be used to simplify the application of Conley index techniques even further. We also hope that our results provide a better bridge between the different fields. Furthermore we show how to interpret Conley's conditions in terms of averaging. The result are illustrated by the two-dimensional van der Pol equation and by a three-dimensional Morris-Lecar model.

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