  In this paper, we investigate convergence of a class of analytic neural
networks with event-triggered rule. This model is general and include Hopfield
neural network as a special case. The event-trigger rule efficiently reduces
the frequency of information transmission between synapses of the neurons. The
synaptic feedback of each neuron keeps a constant value based on the outputs of
its neighbours at its latest triggering time but changes until the next
triggering time of this neuron that is determined by certain criterion via its
neighborhood information. It is proved that the analytic neural network is
completely stable under this event-triggered rule. The main technique of proof
is the ${\L}$ojasiewicz 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
theoretical results and present the optimisation capability of the network
dynamics.
