Electron. J. Diff. Equ., Vol. 2013 (2013), No. 252, pp. 1-12.

Bogdanov-Takens bifurcation for neutral functional differential equations

Jianzhi Cao, Rong Yuan

Abstract:
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.

Submitted August 6, 2013. Published November 20, 2013.
Math Subject Classifications: 34K06, 34K18, 34K20, 34K60, 37G05, 37G10.
Key Words: Neutral functional differential equations; center manifold; Bogdanov-Takens bifurcation; normal forms.

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Jianzhi Cao
School of Mathematical Sciences
Beijing Normal University
Beijing 100875, China
email: cjz2004987@163.com
Rong Yuan
School of Mathematical Sciences
Beijing Normal University
Beijing 100875, China
email: ryuan@bnu.edu.cn

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