BIFURCATIONS, STABILITY, AND MONOTONICITY PROPERTIES OF A DELAYED NEURAL-NETWORK MODEL

A delay-differential equation modelling an artificial neural network w ith two neurons is investigated. A linear stability analysis provides parameter values yielding asymptotic stability of the stationary solut ions: these can lose stability through either a pitchfork or a Hopf bi furcation, which is shown to be supercritical. At appropriate paramete r values, an interaction takes place between the pitchfork and Hopf bi furcations. Conditions are also given for the set of initial condition s that converge to a stable stationary solution to be open and dense i n the functional phase space. Analytic results are illustrated with nu merical simulations.