Tenth MSU Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 23 (2016), pp. 175-187.

Bogdanov-Takens singularity of a neural network model with delay

Xiaoqin P. Wu

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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