Global Hopf bifurcation analysis of a six-dimensional Fitzhugh-Nagumo neural network with delay by a synchronized scheme

Fang Han, Bin Zhen, Ying Du, Yanhong Zheng, Marian Wiercigroch

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1 Citation (Scopus)

Abstract

Global Hopf bifurcation analysis is carried out on a six-dimensional FitzHugh-Nagumo (FHN) neural network with a time delay. First, the existence of local Hopf bifurcations of the system is investigated and the explicit formulae which can determine the direction of the bifurcations and the stability of the periodic solutions are derived using the normal form method and the center manifold theory. Then the sufficient conditions for the system to have multiple periodic solutions when the delay is far away from the critical values of Hopf bifurcations are obtained by using the Wu's global Hopf bifurcation theory and the Bendixson's criterion. Especially, a synchronized scheme is used during the analysis to reduce the dimension of the system. Finally, example numerical simulations are given to support the theoretical analysis.

Original languageEnglish
Pages (from-to)457-474
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - B
Volume16
Issue number2
DOIs
Publication statusPublished - Sep 2011

Keywords

  • Global Hopf bifurcation
  • FitzHugh-Nagumo model
  • neural network
  • delay
  • synchronize

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