Some dynamical properties for a class of discrete recurrent neural networks

This paper studies some dynamical properties of a class of discrete recurrent neural networks. It addresses non-divergence, global attractivity, and complete stability of the networks. Conditions for non-divergence are derived, which not only guarantee non-divergence but also allow for the existence of multi-equilibrium points. Under these nondivergence conditions, global attracting compact sets are obtained. Complete stability is studied via a novel energy function and the Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.