A weak condition for global stability of delayed neural networks

Ricai  Luo; Honglei Xu; Wu-Sheng  Wang; Jie  Sun; Wei  Xu

doi:10.3934/jimo.2016.12.505

Article Contents

2016, Volume 12, Issue 2: 505-514. Doi: 10.3934/jimo.2016.12.505

This issue Previous Article Fiscal centralization vs. decentralization on economic growth and welfare: An optimal-control approach Next Article A combinatorial optimization approach to the selection of statistical units

A weak condition for global stability of delayed neural networks

1.
School of Computer and Information Engineering, Hechi University, Guangxi, Yizhou 546300
2.
Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845
3.
School of Mathematics and Statistics, Hechi University, Guangxi, Yizhou 546300
4.
Department of Mathematics and Statistics, Curtin University, Perth,WA 6845
5.
School of Information Science and Engineering, Central South University, Changsha, Hunan 410083

Received: September 2014

Revised: February 2015

Published: April 2016

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Abstract

The classical analysis of asymptotical and exponential stability of neural networks needs assumptions on the existence of a positive Lyapunov function $V$ and on the strict negativity of the function $dV/dt$, which often come as a result of boundedness or uniformly almost periodicity of the activation functions. In this paper, we investigate the asymptotical stability problem of Hopfield neural networks with time delays under weaker conditions. By constructing a suitable Lyapunov function, sufficient conditions are derived to guarantee global asymptotical stability and exponential stability of the equilibrium of the system. These conditions do not require the strict negativity of $dV/dt $, nor do they require that the activation functions to be bounded or uniformly almost periodic.

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Mathematics Subject Classification: 93D20, 93C10; Secondary: 92B20.

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