Bogdanov-takens Bifurcation for Neutral Functional Differential Equations

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 Magalhães [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 ilustrate the theoretical results.