A study on WTA cellular neural networks

This paper addresses a number of basic issues concerning the dynamics of a class of winner‐take‐all cellular neural networks (WTA CNNs) proposed by Seiler and Nossek. The main result is an analytical estimate for the settling time, which shows from a theoretical point of view that such CNNs are well suited for on‐line applications requiring a large number of units, fast processing speed and a relatively high resolution. Other results are the determination of the largest parameter set that guarantee a correct WTA functionality for all initial conditions and the solution of a conjecture made by Seiler and Nossek. These results are proved by means of a new Lyapunov function to analyse the global dynamical behaviour of the WTA CNNs.