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http://hdl.handle.net/1942/42694
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DC Field | Value | Language |
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dc.contributor.author | BOSSCHAERT, Maikel | - |
dc.contributor.author | Kuznetsov, Yuri A. | - |
dc.date.accessioned | 2024-03-27T08:10:00Z | - |
dc.date.available | 2024-03-27T08:10:00Z | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-03-27T07:59:14Z | - |
dc.identifier.citation | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 23 (1) , p. 410 -439 | - |
dc.identifier.issn | 1536-0040 | - |
dc.identifier.uri | http://hdl.handle.net/1942/42694 | - |
dc.description.abstract | This paper provides for the first time correct third-order homoclinic predictors in n-dimensional ODEs near a generic Bogdanov-Takens bifurcation point, which can be used to start the numerical continuation of the appearing homoclinic orbits. To achieve this, higher-order time approximations to the nonlinear time transformation in the Lindstedt--Poincare'\ method are essential. Moreover, a correct transform between approximations to solutions in the normal form and approximations to solutions on the parameter -dependent center manifold is derived rigorously. A detailed comparison is done between applying different normal forms (smooth and orbital), different phase conditions, and different perturbation methods (regular and Lindstedt--Poincare'\) to approximate the homoclinic solution near Bogdanov-Takens points. Examples demonstrating the correctness of the predictors are given. The new homoclinic predictors are implemented in the open -source MATLAB/GNU Octave continuation package MatCont. | - |
dc.description.sponsorship | The authors would like to thank Prof. Peter De Maesschalck (Hasselt University, Belgium) for multiple useful discussions during this research project, Prof. Wolf-Jürgen Beyn (Bielefeld University, Germany) for his positive comments on the preprint, and Dr. Hil Meijer (University of Twente, The Netherlands) for multiple suggestions leading to a significant improvement of the paper. Additionally, we would like to express our gratitude to the two anonymous referees for very useful remarks and suggestions. | - |
dc.language.iso | en | - |
dc.publisher | SIAM PUBLICATIONS | - |
dc.subject.other | Bogdanov-Takens bifurcation | - |
dc.subject.other | homoclinic asymptotics | - |
dc.subject.other | center manifold reduction | - |
dc.title | Interplay between Normal Forms and Center Manifold Reduction for Homoclinic Predictors near Bogdanov-Takens Bifurcation | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 439 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 410 | - |
dc.identifier.volume | 23 | - |
local.format.pages | 30 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Bosschaert, MM (corresponding author), Hasselt Univ, Dept Math, B-3590 Diepenbeek, Belgium. | - |
dc.description.notes | maikel.bosschaert@uhasselt.be; i.a.kouznetsov@uu.nl | - |
local.publisher.place | 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1137/22M151354X | - |
dc.identifier.isi | 001171420800002 | - |
dc.identifier.eissn | - | |
local.provider.type | wosris | - |
local.description.affiliation | [Bosschaert, Maikel M.] Hasselt Univ, Dept Math, B-3590 Diepenbeek, Belgium. | - |
local.description.affiliation | [Kuznetsov, Yuri A.] Univ Utrecht, Dept Math, NL-3508 TA Utrecht, Netherlands. | - |
local.description.affiliation | [Kuznetsov, Yuri A.] Univ Twente, Dept Appl Math, NL-7500 AE Enschede, Netherlands. | - |
local.uhasselt.international | yes | - |
item.fulltext | No Fulltext | - |
item.accessRights | Closed Access | - |
item.contributor | BOSSCHAERT, Maikel | - |
item.contributor | Kuznetsov, Yuri A. | - |
item.fullcitation | BOSSCHAERT, Maikel & Kuznetsov, Yuri A. (2024) Interplay between Normal Forms and Center Manifold Reduction for Homoclinic Predictors near Bogdanov-Takens Bifurcation. In: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 23 (1) , p. 410 -439. | - |
crisitem.journal.issn | 1536-0040 | - |
Appears in Collections: | Research publications |
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