Discrete Dynamics in Nature and Society
Volume 2005 (2005), Issue 3, Pages 281-297

Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks

Hong Xiang, Ke-Ming Yan, and Bai-Yan Wang

Institute of Applied Mathematics, Lanzhou University of Technology, Gansu, Lanzhou 730050, China

Received 6 February 2005

Copyright © 2005 Hong Xiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By using coincidence degree theory as well as a priori estimates and Lyapunov functional, we study the existence and global stability of periodic solution for discrete delayed high-order Hopfield-type neural networks. We obtain some easily verifiable sufficient conditions to ensure that there exists a unique periodic solution, and all theirs solutions converge to such a periodic solution.