Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 196, Issue 2, Pages 579-595Publisher
ELSEVIER
DOI: 10.1016/j.cam.2005.10.012
Keywords
neural network; time delay; stability; Hopf bifurcation; periodic solutions
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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. (c) 2005 Elsevier B.V. All rights reserved.
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