Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays

  • Michael Y. LiEmail author
  • Junjie Wei
Part of the Fields Institute Communications book series (FIC, volume 64)


For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the bifurcation points, we establish that local Hopf branches globally extend for arbitrarily large delays.



Research of MYL is supported in part by grants from Natural Sciences and Engineering Council (NSERC) and Canada Foundation for Innovation (CFI). Research of JW is supported in part by grants from the National Science Foundation of China (NSFC)

Received 3/18/2009; Accepted 8/22/2010


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of MathematicsHarbin Institute of TechnologyHarbinP. R. China

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