Interval methods for solving cellular neural networks (CNNs) equations

In this paper the problem of finding all equilibrium points in CNNs is considered. The problem is of a great importance because the equilibrium points are connected with the “output capacity” of the network. They set the limits on the number of different outcomes and this may be critical in applications such as filtering, classification or feature extraction. CNNs are nonlinear circuits and well known methods for determining all DC solutions in nonlinear circuits (piece-wise linear techniques, path following procedures, etc.) are usually used for finding all equilibrium points in CNNs. The specific description of CNNs allows for some new methods. In this paper the interval methods for finding all de solutions in nonlinear circuits are applied for solving the problem. The specific type of CNNs equations is used to achieve some improvements of the methods. Two examples are given that confirms the efficiency of applying interval methods for solving CNNs equations