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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/21884

Title: The entry-exit function and geometric singular perturbation theory
Authors: De Maesschalck, Peter
Schecter, Stephen
Issue Date: 2016
Citation: JOURNAL OF DIFFERENTIAL EQUATIONS, 260 (8), p. 6697-6715
Abstract: For small epsilon > 0, the system (x) over dot = epsilon, (z) over dot = h(x, z, s)z, with h(x, 0, 0) < 0 for x < 0 and h(x, 0, 0) > 0 for x > 0, admits solutions that approach the x-axis while x < 0 and are repelled from it when x > 0. The limiting attraction and repulsion points are given by the well-known entry-exit function. For h(x, z, s)z replaced by h(x, z, epsilon)z(2), we explain this phenomenon using geometric singular perturbation theory. We also show that the linear case can be reduced to the quadratic case, and we discuss the smoothness of the return map to the line z = z(0), z(0) > 0, in the limit epsilon -> 0. (C) 2016 Elsevier Inc. All rights reserved.
Notes: [De Maesschalck, Peter] Hasselt Univ, Dept Math & Stat, B-3590 Diepenbeek, Belgium. [Schecter, Stephen] N Carolina State Univ, Dept Math, Box 8205, Raleigh, NC 27695 USA.
URI: http://hdl.handle.net/1942/21884
DOI: 10.1016/j.jde.2016.01.008
ISI #: 000371450000009
ISSN: 0022-0396
Category: A1
Type: Journal Contribution
Validation: ecoom, 2017
Appears in Collections: Research publications

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