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http://hdl.handle.net/1942/22607
Title: | Regular and slow-fast codimension 4 saddle-node bifurcations | Authors: | HUZAK, Renato | Issue Date: | 2017 | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 262 (2), p. 1119-1154 | Abstract: | Using geometric singular perturbation theory, including the family blow-up as one of the main techniques, we prove that the cyclicity, i.e. maximum number of limit cycles, in both regular and slow-fast unfoldings of nilpotent saddle-node singularity of codimension 4 is 2. The blow-up technique enables us to use the well known results for slow-fast codimension 1 and 2 Hopf bifurcations, slow-fast Bogdanov–Takens bifurcations and slow-fast codimension 3 saddle and elliptic bifurcations. | Notes: | Huzak, R (reprint author), Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. renato.huzak@uhasselt.be | Keywords: | blow-up; limit cycles; singular perturbations; slow-fast systems | Document URI: | http://hdl.handle.net/1942/22607 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2016.10.008 | ISI #: | 000389682300012 | Rights: | © 2016 Elsevier Inc. All rights reserved | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2018 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
SlowFastCodimensionFour.pdf | Peer-reviewed author version | 1.63 MB | Adobe PDF | View/Open |
1-s2.0-S0022039616303333-main.pdf Restricted Access | Published version | 1.39 MB | Adobe PDF | View/Open Request a copy |
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