Global Hopf bifurcation analysis of a six-dimensional FitzHugh-Nagumo neural network with delay by a synchronized scheme
2011
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.
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