Stability and Hopf bifurcation analysis on a ring of four neurons with delays

We consider a four-neuron ring with self-feedback and delays. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are presented to illustrate the results. (C) 2009 Elsevier Inc. All rights reserved.