Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium...

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Main Authors: Yanyan Wang, Jianping Zhou
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/109319
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spelling doaj-943bdcfdb1764f26908e1d6f2ae49daa2020-11-24T22:38:52ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/109319109319Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation FunctionsYanyan Wang0Jianping Zhou1School of Mathematics and Physics, Anhui University of Technology, Ma'anshan 243002, ChinaSchool of Computer Science, Anhui University of Technology, Ma'anshan 243002, ChinaCohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.http://dx.doi.org/10.1155/2012/109319
collection DOAJ
language English
format Article
sources DOAJ
author Yanyan Wang
Jianping Zhou
spellingShingle Yanyan Wang
Jianping Zhou
Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
Abstract and Applied Analysis
author_facet Yanyan Wang
Jianping Zhou
author_sort Yanyan Wang
title Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
title_short Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
title_full Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
title_fullStr Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
title_full_unstemmed Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
title_sort global convergence for cohen-grossberg neural networks with discontinuous activation functions
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.
url http://dx.doi.org/10.1155/2012/109319
work_keys_str_mv AT yanyanwang globalconvergenceforcohengrossbergneuralnetworkswithdiscontinuousactivationfunctions
AT jianpingzhou globalconvergenceforcohengrossbergneuralnetworkswithdiscontinuousactivationfunctions
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