A winner-take-all Lotka---Volterra recurrent neural network with only one winner in each row and each column

A winner-take-all Lotka---Volterra recurrent neural network with N × N neurons is proposed in this paper. Sufficient conditions for existence of winner-take-all stable equilibrium points in the network are obtained. These conditions guarantee that there is one and only one winner in each row and each column at any stable equilibrium point. In addition, rigorous convergence analysis is carried out. It is proven that the proposed network model is convergent. The conditions for the winner-take-all behavior obtained in this paper provide design guidelines for network implementation and fabrication. Simulations are also presented to illustrate the theoretical findings.