Geodesic
Bogdanov-Takens bifurcation for neutral functional differential equations
Electronic journal of differential equations, Tome 2013 (2013)
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__a133,
     author = {Cao,  Jianzhi and Yuan,  Rong},
     title = {Bogdanov-Takens bifurcation for neutral functional differential equations},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1293.34089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a133/}
}
TY  - JOUR
AU  - Cao,  Jianzhi
AU  - Yuan,  Rong
TI  - Bogdanov-Takens bifurcation for neutral functional differential equations
JO  - Electronic journal of differential equations
PY  - 2013
VL  - 2013
UR  - http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a133/
LA  - en
ID  - EJDE_2013__2013__a133
ER  - 
%0 Journal Article
%A Cao,  Jianzhi
%A Yuan,  Rong
%T Bogdanov-Takens bifurcation for neutral functional differential equations
%J Electronic journal of differential equations
%D 2013
%V 2013
%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a133/
%G en
%F EJDE_2013__2013__a133
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__a133/