Mathematical analysis of neural networks used in the solution of set selection problems

Abstract

The generalized neural network model of M. Cohen and S. Grossberg (1983) has been studied by many authors using Lyapunov-type functions. As an alternative, the author treats closely related dynamical systems (the gain functions are piecewise linear) with other dynamical-systems-theory machinery. It is shown that, by using a certain perturbation scheme, one can use such models with piecewise linear gain functions to solve a variety of set selection problems.<>