Bogdanov-Takens singularity of a neural network model with delay

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.

Keywords

• Tree-neuron model with time delay
• BT singularity
• Hopf bifurcation
• double limit cycle bifurcation
• triple limit cycle bifurcation