Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/27416
Title: | Slow divergence integral on a Möbius band | Authors: | HUZAK, Renato | Issue Date: | 2018 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 266 (10), p. 6179-6203. | Status: | In Press | Abstract: | The slow divergence integral has proved to be an important tool in the study of slow-fast cycles defined on an orientable two-dimensional manifold (e.g. R^2). The goal of our paper is to study 1-canard cycle and 2-canard cycle bifurcations on a non-orientable two-dimensional manifold (e.g. the Möbius band) by using similar techniques. Our focus is on smooth slow-fast models with a Hopf breaking mechanism. The same results can be proved for a jump breaking mechanism and non-generic turning points. The slow-fast bifurcation problems on the Möbius band require the study of the 2-return map attached to such 1- and 2-canard cycles. We give a simple sufficient condition, expressed in terms of the slow divergence integral, for the existence of a period-doubling bifurcation near the 1-canard cycle. We also prove the finite cyclicity property of “singular” 1- and 2-homoclinic loops (“regular” 1-homoclinic loops of finite codimension have been studied by Guimond). | Keywords: | slow divergence integral; Mobius band; slow-fast systems | Document URI: | http://hdl.handle.net/1942/27416 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2018.11.002 | ISI #: | WOS:000459921400001 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2020 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
SDIMobius.pdf | Peer-reviewed author version | 954.73 kB | Adobe PDF | View/Open |
1-s2.0-S002203961830648X-main.pdf Restricted Access | Published version | 738.24 kB | Adobe PDF | View/Open Request a copy |
WEB OF SCIENCETM
Citations
1
checked on Apr 30, 2024
Page view(s)
42
checked on Sep 7, 2022
Download(s)
14
checked on Sep 7, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.