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 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | 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. | Keywords: | Entry-exit function; Geometric singular perturbation theory; Bifurcation delay; Blow-up; Turning point;entry–exit function; geometric singular perturbation theory; bifurcation delay; blow-up; turning point | Document URI: | http://hdl.handle.net/1942/21884 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2016.01.008 | ISI #: | 000371450000009 | Rights: | © 2016 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2017 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
de maesschalck 1.pdf Restricted Access | Published version | 382.72 kB | Adobe PDF | View/Open Request a copy |
SCOPUSTM
Citations
16
checked on Sep 2, 2020
WEB OF SCIENCETM
Citations
54
checked on Aug 11, 2024
Page view(s)
120
checked on Sep 7, 2022
Download(s)
102
checked on Sep 7, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.