Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions

This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piece-wise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.