  In this paper, we first address the dynamics of the elegant multi-valued
quaternionic Hopfield neural network (MV-QHNN) proposed by Minemoto and
collaborators. Contrary to what was expected, we show that the MV-QHNN, as well
as one of its variation, does not always come to rest at an equilibrium state
under the usual conditions. In fact, we provide simple examples in which the
network yields a periodic sequence of quaternionic state vectors. Afterward, we
turn our attention to the continuous-valued quaternionic Hopfield neural
network (CV-QHNN), which can be derived from the MV-QHNN by means of a limit
process. The CV-QHNN can be implemented more easily than the MV-QHNN model.
Furthermore, the asynchronous CV-QHNN always settles down into an equilibrium
state under the usual conditions. Theoretical issues are all illustrated by
examples in this paper.
