Keywords: PatRec

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### Theory of the Network

The equations that are used to determine the states of the units are based on the results of Grossberg's research into systems of differential equations. The principal theoretical result underpinning the operation of the ART networks is the Cohen-Grossberg Stability Theorem. This is a very general and technical result about a class of ordinary differential equations. In the context of ART, it guarantees that the units in the output layer will reach a steady state and not oscillate periodically or chaotically.