Xiaoqin P. Wu
Abstract:
In this article, we study Bogdanov-Takens (BT) singularity of a tree-neuron
model with time delay. By using the frameworks of Campbell-Yuan [2]
and Faria-Magalhaes [4,5], the normal form on the center manifold
is derived for this singularity and hence the corresponding bifurcation
diagrams such as Hopf, double limit cycle, and triple limit cycle bifurcations
are obtained. Examples are given to verify some theoretical results.
Published March 21, 2016.
Math Subject Classifications: 92B20, 34F10.
Key Words: Tree-neuron model with time delay; BT singularity; Hopf bifurcation;
double limit cycle bifurcation; triple limit cycle bifurcation.
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Xiaoqin P. Wu Department of Mathematics Computer & Information Sciences Mississippi Valley State University Itta Bena, MS 38941, USA email: xpwu@mvsu.edu |
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