Asymptotic Stability, Orbital Stability of Hopf-Bifurcating Periodic Solution of a Simple Three-Neuron Artificial Neural Network with Distributed Delay

Abstract. A distributed delay model of a class of three-neuron network has been investigated. Sufficient conditions for existence of uniqu e equilibrium, multiple equilibria and their local stability are derived. A closed interval for a parameter of the system is identified in which Hopf-bifurcating periodic solution o ccurs for each point of such interval. The orbital stability of such bifurcating period c solution at the extreme points of the interval is ascertained. Lastly global bifurcation a spect of such periodic solutions is studied. The results are illustrated by numerical simula tions.

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