Advances in Difference Equations
Volume 2009 (2009), Article ID 798685, 14 pages
Research Article

Global Stability Analysis for Periodic Solution in Discontinuous Neural Networks with Nonlinear Growth Activations

1College of Information Science and Engineering, Yanshan University, Qinhuangdao 066004, China
2Department of Applied Mathematics, Yanshan University, Qinhuangdao 066004, China

Received 30 December 2008; Accepted 18 March 2009

Academic Editor: Toka Diagana

Copyright © 2009 Yingwei Li and Huaiqin Wu. 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.


This paper considers a new class of additive neural networks where the neuron activations are modelled by discontinuous functions with nonlinear growth. By Leray-Schauder alternative theorem in differential inclusion theory, matrix theory, and generalized Lyapunov approach, a general result is derived which ensures the existence and global asymptotical stability of a unique periodic solution for such neural networks. The obtained results can be applied to neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also show that Forti's conjecture for discontinuous neural networks with nonlinear growth activations is true.