Analysis and synthesis of a class of neural networks: variable structure systems with infinite grain

An investigation was conducted of the qualitative properties of a class of neural networks described by a system of first-order ordinary differential equations with discontinuous right hand side. An efficient synthesis procedure is developed for this class of neural networks. The class of systems considered may be used as a representation of the analog Hopfield model with the nonlinearities having infinite gain. Also, under appropriate assumptions, the output of the class of systems considered may be viewed as representing the behavior of the discrete Hopfield model. Thus the results give insight into the qualitative behavior of the analog as well as the discrete Hopfield models, and they provide a means of designing such models. The applicability of the present results is demonstrated by several specific examples