Dynamic Analysis of a General Class of Winner-Take-All Competitive Neural Networks

This paper studies a general class of dynamical neural networks with lateral inhibition, exhibiting winner-take-all (WTA) behavior. These networks are motivated by a metal-oxide-semiconductor field effect transistor (MOSFET) implementation of neural networks, in which mutual competition plays a very important role. We show that for a fairly general class of competitive neural networks, WTA behavior exists. Sufficient conditions for the network to have a WTA equilibrium are obtained, and rigorous convergence analysis is carried out. The conditions for the network to have the WTA behavior obtained in this paper provide design guidelines for the network implementation and fabrication. We also demonstrate that whenever the network gets into the WTA region, it will stay in that region and settle down exponentially fast to the WTA point. This provides a speeding procedure for the decision making: as soon as it gets into the region, the winner can be declared. Finally, we show that this WTA neural network has a self-resetting property, and a resetting principle is proposed.