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Title: | Bifurcation Analysis of Bogdanov-Takens Bifurcations in Delay Differential Equations | Authors: | BOSSCHAERT, Maikel Kuznetsov, Yu. A. |
Issue Date: | 2024 | Publisher: | SIAM PUBLICATIONS | Source: | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 23 (1) , p. 553 -591 | Abstract: | In this paper, we will perform the parameter -dependent center manifold reduction near the generic and transcritical codimension two Bogdanov-Takens bifurcation in classical delay differential equations. Using an approximation to the homoclinic solutions derived with a generalized Lindstedt-Poincare'\ method, we develop a method to initialize the continuation of the homoclinic bifurcation curves emanating from these points. The normal form transformation is derived in the functional analytic perturbation framework for dual semigroups (sun -star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas, which have been implemented in the freely available bifurcation software package DDE-BifTool. The effectiveness is demonstrated on various models | Notes: | Bosschaert, MM (corresponding author), Hasselt Univ, Dept Math, Diepenbeek Campus,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium. maikel.bosschaert@uhasselt.be; I.A.Kouznetsov@uu.nl |
Keywords: | generic Bogdanov-Takens bifurcation;transcritical Bogdanov-Takens bifurcation;homoclinic solutions;delay differential equations;sun-star calculus;strongly continuous semigroups;center manifold theorem;DDE-BifTool | Document URI: | http://hdl.handle.net/1942/42672 | ISSN: | 1536-0040 | DOI: | 10.1137/22M1527532 | ISI #: | 001171420800011 | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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