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http://hdl.handle.net/1942/21884
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DC Field | Value | Language |
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dc.contributor.author | DE MAESSCHALCK, Peter | - |
dc.contributor.author | Schecter, Stephen | - |
dc.date.accessioned | 2016-07-26T08:12:01Z | - |
dc.date.available | 2016-07-26T08:12:01Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | JOURNAL OF DIFFERENTIAL EQUATIONS, 260 (8), p. 6697-6715 | - |
dc.identifier.issn | 0022-0396 | - |
dc.identifier.uri | http://hdl.handle.net/1942/21884 | - |
dc.description.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. | - |
dc.description.sponsorship | This work was partly supported by FWO project G093910 (De Maesschalck) and NSF grant DMS-1211707 (Schecter). We thank the referee for a careful reading of the paper, which led to a number of clarifications and corrections. | - |
dc.language.iso | en | - |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | - |
dc.rights | © 2016 Elsevier Inc. All rights reserved. | - |
dc.subject.other | Entry-exit function; Geometric singular perturbation theory; Bifurcation delay; Blow-up; Turning point | - |
dc.subject.other | entry–exit function; geometric singular perturbation theory; bifurcation delay; blow-up; turning point | - |
dc.title | The entry-exit function and geometric singular perturbation theory | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 6715 | - |
dc.identifier.issue | 8 | - |
dc.identifier.spage | 6697 | - |
dc.identifier.volume | 260 | - |
local.format.pages | 19 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.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. | - |
local.publisher.place | SAN DIEGO | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1016/j.jde.2016.01.008 | - |
dc.identifier.isi | 000371450000009 | - |
item.fullcitation | DE MAESSCHALCK, Peter & Schecter, Stephen (2016) The entry-exit function and geometric singular perturbation theory. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 260 (8), p. 6697-6715. | - |
item.contributor | DE MAESSCHALCK, Peter | - |
item.contributor | Schecter, Stephen | - |
item.validation | ecoom 2017 | - |
item.accessRights | Restricted Access | - |
item.fulltext | With Fulltext | - |
crisitem.journal.issn | 0022-0396 | - |
crisitem.journal.eissn | 1090-2732 | - |
Appears in Collections: | Research publications |
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de maesschalck 1.pdf Restricted Access | Published version | 382.72 kB | Adobe PDF | View/Open Request a copy |
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