Stability of Analytic Neural Networks with Event-triggered Synaptic Feedbacks

TL;DR

This paper analyzes the stability of a broad class of analytic neural networks with event-triggered synaptic feedback, demonstrating convergence to equilibrium and efficiency in computation and communication.

Contribution

It introduces a general event-triggered feedback mechanism for neural networks, including Hopfield networks, and proves their stability and convergence.

Findings

All trajectories converge to equilibrium for almost all initial conditions.

Event-triggered rules reduce computational and communication loads.

Numerical examples confirm theoretical stability and efficiency.

Abstract

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.