Equilibrium characterization of dynamical neural networks and a systematic synthesis procedure for associative memories

Several novel results concerning the characterization of the equilibrium conditions of a continuous-time dynamical neural network model and a systematic procedure for synthesizing associative memory networks with nonsymmetrical interconnection matrices are presented. The equilibrium characterization focuses on the exponential stability and instability properties of the network equilibria and on equilibrium confinement, viz., ensuring the uniqueness of an equilibrium in a specific region of the state space. While the equilibrium confinement result involves a simple test, the stability results given obtain explicit estimates of the degree of exponential stability and the regions of attraction of the stable equilibrium points. Using these results as valuable guidelines, a systematic synthesis procedure for constructing a dynamical neural network that stores a given set of vectors as the stable equilibrium points is developed