Geodesic
Bogdanov-Takens bifurcation for neutral functional differential equations
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we consider a class of neutral functional differential equations (NFDEs). First, some feasible assumptions and algorithms are given for the determination of Bogdanov-Takens (B-T) singularity. Then, by employing the method based on center manifold reduction and normal form theory due to Faria and Magalhaes [4], a concrete reduced form for the parameterized NFDEs is obtained and the bifurcation behavior of the parameterized NFDEs is described. This result extend the B-T bifurcation analysis reported in [16]. Finally, two examples illustrate the theoretical results.
Classification : 34K06, 34K18, 34K20, 34K60, 37G05, 37G10
Keywords: neutral functional differential equations, center manifold, bogdanov-Takens bifurcation, normal forms 
@article{EJDE_2013__2013__a33,
     author = {Cao, Jianzhi and Yuan, Rong},
     title = {Bogdanov-Takens bifurcation for neutral functional differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a33/}
}
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Cao, Jianzhi; Yuan, Rong. Bogdanov-Takens bifurcation for neutral functional differential equations. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a33/