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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