Hopf-Zero Bifurcation in Three-Cell Networks with Two Discrete Time Delays

Abstract

In this paper, we study a delayed three-cell network which is introduced by coupled cell theory and neural network theory. We investigate this model with two different discrete delays. The aim is to obtain necessary conditions for the stability and the existence of Hopf-zero bifurcation in this model. Moreover, we find the normal form of this bifurcation by using linearization and the Multiple Time Scale method. Finally, the theoretical results are verified by numerical simulations.

Keywords

• coupled cell theory
• neural network
• stability
• hopf-zero bifurcation
• normal form