Analysis and synthesis of a class of neuron networks: linear systems operating in saturated modes

Abstract

An investigation was conducted of the qualitative properties of a class of neural networks described by a system of first-order linear ordinary differential equations which are defined on a closed hypercube of the state space with solutions extended to the boundary of the hypercube. When solutions are located on the boundary of the hypercube, the system is said to be in a saturated mode. The class of systems considered retains the basic structure of the Hopfield model but is easier to analyze, synthesize, and implement. An efficient analysis method is developed which can be used to completely determine the set of asymptotically stable equilibrium points and the set of unstable equilibrium points. The latter set can be used to estimate the domains of attraction for the elements of the former set. A synthesis procedure that was developed previously by the authors is modified and applied to the present class of neural networks. The class of systems considered herein can easily be implemented in analog integrated circuits. >