Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales

Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales

We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of...

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Main Authors: Yaping Ren, Yongkun Li
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2012/386706
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spelling doaj-e7f04074648045f7bff6c35a35b84fc92020-11-24T20:47:04ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/386706386706Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time ScalesYaping Ren0Yongkun Li1School of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, ChinaDepartment of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaWe study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of the previously known results.http://dx.doi.org/10.1155/2012/386706
collection DOAJ
language English
format Article
sources DOAJ
author Yaping Ren
Yongkun Li
spellingShingle Yaping Ren
Yongkun Li
Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
Discrete Dynamics in Nature and Society
author_facet Yaping Ren
Yongkun Li
author_sort Yaping Ren
title Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
title_short Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
title_full Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
title_fullStr Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
title_full_unstemmed Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
title_sort stability and existence of periodic solutions for cellular neural networks with state dependent delays on time scales
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2012-01-01
description We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of the previously known results.
url http://dx.doi.org/10.1155/2012/386706
work_keys_str_mv AT yapingren stabilityandexistenceofperiodicsolutionsforcellularneuralnetworkswithstatedependentdelaysontimescales
AT yongkunli stabilityandexistenceofperiodicsolutionsforcellularneuralnetworkswithstatedependentdelaysontimescales
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