Volume 4, Issue 3, September 2018, Page: 78-83
Global Asymptotic Stability for a New Class of Neutral Neural Networks
Ricai Luo, School of Mathematics and Statistics, Hechi University, Yizhou, China
Gang Lin, School of Design and Built Environment, Curtin University, Perth, Australia
Dongdong Yin, School of Mathematics and Statistics, Hechi University, Yizhou, China
Received: Aug. 28, 2018;       Accepted: Oct. 17, 2018;       Published: Nov. 9, 2018
DOI: 10.11648/j.ijamtp.20180403.13      View  135      Downloads  13
Abstract
In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.
Keywords
Global Asymptotic Stability, Neutral Neural Network, Time-Varying Delay, Sufficient Condition
To cite this article
Ricai Luo, Gang Lin, Dongdong Yin, Global Asymptotic Stability for a New Class of Neutral Neural Networks, International Journal of Applied Mathematics and Theoretical Physics. Vol. 4, No. 3, 2018, pp. 78-83. doi: 10.11648/j.ijamtp.20180403.13
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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