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 · Discrete and Continuous Dynamical Systems - B · 2011
Global Hopf bifurcation analysis is carried out on a six-dimensionalFitzHugh-Nagumo (FHN) neural network with a time delay. First, theexistence of local Hopf bifurcations of the system is investigatedand the explicit formulae which can determine the direction of thebifurcations and the stability of the periodic solutions are derivedusing the normal form method and the center manifold theory. Thenthe sufficient conditions for the system to have multiple periodicsolutions when the delay is far away from the critical values ofHopf bifurcations are obtained by using the Wu's global Hopfbifurcation theory and the Bendixson's criterion. Especially, asynchronized scheme is used during the analysis to reduce thedimension of the system. Finally, example numerical simulations aregiven to support the theoretical analysis.