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The Conley Index for Fast-Slow Systems I. One-Dimensional Slow Variable |
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| Authors: | Tomáš Gedeon Hiroshi Kokubu Konstantin Mischaikow Hiroe Oka James F Reineck |
| Institution: | (1) Department of Mathematical Sciences, Montana State University, Bozeman, Montana, 59717-0240;(2) Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan;(3) Center for Dynamical Systems and Nonlinear Studies, School of Mathematics, Georgia Institute of technology, Atlanta, Georgia, 30332;(4) Department of Applied Mathematics and Informatics, Faculty of Science and technology, Ryukoku University, Seta, Otsu, 520-2194, Japan;(5) Department of mathematics, SUNY at Buffalo, Buffalo, New York, 14214-3093 |
| Abstract: | We develop a qualitative theory for fast-slow systems with a one-dimensional slow variable. Using Conley index theory for singularity perturbed systems, conditions are given which imply that if one can construct heteroclinic connections and periodic orbits in systems with the derivative of the slow variable set to 0, these orbits persist when the derivative of the slow variable is small and nonzero. |
| Keywords: | Fast-slow systems Conley index heteroclinic connection periodic orbit |
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