Periodic dynamics of multidirectional associative neural networks with discontinuous activation functions and mixed time delays

Abstract

AbstractMultidirectional associative memory neural networks (MAMNNs) are constructed to simulate the many‐to‐many association, and they are applied widely in many fields. It is important to explore the global stability of the periodic solution of MAMNNs. In this paper, MAMNNs with discontinuous activation functions and mixed time‐varying delays are considered. Firstly, we investigate the conditions for the existence of the periodic solution by using the Mawhin‐like coincidence theorem, and a special connecting weight matrix is constructed to prove the existence of the periodic solution. Secondly, the uniqueness and global exponential stability of the periodic solution are explored for the non‐self‐connected system by introducing a Lipschitz‐like condition. Finally, numerical simulations are given to illustrate the effectiveness of our main results.