Advances in Difference Equations
Volume 2009 (2009), Article ID 798685, 14 pages
doi:10.1155/2009/798685

Global stability analysis for periodic solution in discontinuous neural networks with nonlinear growth activations

Yingwei Li1 and Huaiqin Wu2

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

Abstract

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.