  In this paper, we investigate stability of a class of analytic neural
networks with the synaptic feedback via event-triggered rules. This model is
general and include Hopfield neural network as a special case. These
event-trigger rules can efficiently reduces loads of computation and
information transmission at synapses of the neurons. The synaptic feedback of
each neuron keeps a constant value based on the outputs of the other neurons at
its latest triggering time but changes at its next triggering time, which is
determined by certain criterion. It is proved that every trajectory of the
analytic neural network converges to certain equilibrium under this
event-triggered rule for all initial values except a set of zero measure. The
main technique of the proof is the Lojasiewicz inequality to prove the
finiteness of trajectory length. The realization of this event-triggered rule
is verified by the exclusion of Zeno behaviors. Numerical examples are provided
to illustrate the efficiency of the theoretical results.
