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In this paper we consider a simple discrete Hopfield neural network model and analyze local stability using the associated characteristic model. In order to study the dynamic behavior of the quasi-periodic orbit, the Hopf bifurcation must be determined. For the case of two neurons, we find one necessary condition that yields the Hopf bifurcation. In addition, we determine the stability and direction of the Hopf bifurcation by applying normal form theory and the center manifold theorem. An example is given and a numerical simulation is performed to illustrate the results. We analyze the influence of bias weights on the stability of the quasi-periodic orbit and study the phase-locking phenomena for certain experimental results with Arnold Tongues in a particular weight configuration., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

A simple two-neuron model of a discrete Hopfield neural network is considered. The local stability is analyzed with the associated characteristic model. In order to study the dynamic behavior, the Fold bifurcation is examined. In the case of two neurons, one necessary condition for yielding the Fold bifurcation is found. In addition, the stability and direction of the fold bifurcation are determined by applying the normal form theory and the center manifold theorem. [ABSTRACT FROM AUTHOR]