Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 252, pp. 1-12.

Title: Bogdanov-Takens bifurcation for neutral functional differential equations

Authors: Jianzhi Cao (Beijing Normal Univ., Beijing, China)
         Rong Yuan   (Beijing Normal Univ., Beijing, China)

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.