Dynamics and stability of generalized cellular nonlinear network model

The aim of this paper is the definition of a new model of neural network, called generalized cellular nonlinear network, that covers architectures and dynamics of the well known and widely used classes of feedforward neural networks and cellular neural networks. We show how cellular neural networks and feedforward neural networks can be derived from the general model: moreover we prove a theorem of existence and uniqueness for the solution of the system that describes the generalized cellular nonlinear network dynamics. These results are obtained using the method of Lyapunov's finite majorizing equations that also represents a new approach in studying the stability of cellular neural networks.