Stability and Bifurcation for a Class of Tri-Neuron Networks With Bidirectionally Delayed Connections and Self-Feedback

Abstract

In this paper, a tri-neuron network with bidirectionally delay and self-feedback is considered. We derive some sufficient conditions dependent or independent of delays for the local stability and instability of this model. Regarding the self-connection delay as the parameter, the Hopf bifurcation analysis is carried out. The direction and stability of the Hopf bifurcation are worked out by applying the normal form theory and the center manifold theory. An example is given and numerical simulations are presented to illustrate the obtained results.