Hopf bifurcation and stability for a delayed tri-neuron network model

Authors:
Xiang-Ping Yan
Affiliations:
School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou, People's Republic of China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

A neural network model with three neurons and a single time delay is considered. Its linear stability is investigated and Hopf bifurcations are demonstrated by analyzing the corresponding characteristic equation. In particular, the explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and the center manifold theorem. In order to illustrate our theoretical analysis, some numerical simulations are also included in the end.