FOLD–HOPF BIFURCATION ANALYSIS FOR A COUPLED FITZHUGH–NAGUMO NEURAL SYSTEM WITH TIME DELAY

Abstract

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered. For a critical case when the corresponding characteristic equation has a single zero root and a pair of purely imaginary roots, a complete bifurcation analysis is presented by employing the center manifold reduction and the normal form method. The Fold–Hopf bifurcation diagrams are provided to illustrate the correctness of our theoretical analysis. Whether almost periodic motion and bursting behavior occur in the FHN neural system with delayed coupling depends on the time delay in the signal transmission between the neurons.