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In this paper, we investigate convergence of a class of analytic neuralnetworks with event-triggered rule. This model is general and include Hopfieldneural network as a special case. The event-trigger rule efficiently reducesthe frequency of information transmission between synapses of the neurons. Thesynaptic feedback of each neuron keeps a constant value based on the outputs ofits neighbours at its latest triggering time but changes until the nexttriggering time of this neuron that is determined by certain criterion via itsneighborhood information. It is proved that the analytic neural network iscompletely stable under this event-triggered rule. The main technique of proofis the ${\L}$ojasiewicz inequality to prove the finiteness of trajectorylength. The realization of this event-triggered rule is verified by theexclusion of Zeno behaviors. Numerical examples are provided to illustrate thetheoretical results and present the optimisation capability of the networkdynamics.

Global Convergence of Analytic Neural Networks with Event-triggered Synaptic Feedbacks