COMPLEX DYNAMICAL BEHAVIORS IN DISCRETE-TIME RECURRENT NEURAL NETWORKS WITH ASYMMETRIC CONNECTION MATRIX

Abstract

This paper investigates the discrete-time recurrent neural networks and aims to extend the previous works with symmetric connection matrix to the asymmetric connection matrix. We provide the sufficient conditions of existence for asymptotical stability of fixed point, flip and fold bifurcations, Marotto's chaos. Besides, we state the conditions of existence for the bounded trapping region including many fixed points, and attracting set contained in bounded region and chaotic set. To demonstrate the theoretical results of the paper, several numerical examples are provided.The theorems in this paper are available more than in the previous works.