Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales

Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales

A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient...

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Main Authors: Yongkun Li, Lei Wang, Yu Fei
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/496396
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spelling doaj-e06eb6ce2ace418dac8e7c4a55fcdb6e2020-11-24T22:06:44ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/496396496396Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time ScalesYongkun Li0Lei Wang1Yu Fei2Department of Mathematics, Yunnan University, Kunming, Yunnan 650221, ChinaDepartment of Mathematics, Yunnan University, Kunming, Yunnan 650221, ChinaSchool of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, ChinaA class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale 𝕋=ℝ or ℤ. Moreover, we present illustrative numerical examples to show the feasibility of our results.http://dx.doi.org/10.1155/2014/496396
collection DOAJ
language English
format Article
sources DOAJ
author Yongkun Li
Lei Wang
Yu Fei
spellingShingle Yongkun Li
Lei Wang
Yu Fei
Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
Journal of Applied Mathematics
author_facet Yongkun Li
Lei Wang
Yu Fei
author_sort Yongkun Li
title Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
title_short Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
title_full Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
title_fullStr Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
title_full_unstemmed Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales
title_sort periodic solutions for shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description A class of shunting inhibitory cellular neural networks of neutral type with time-varying delays in the leakage term on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, fixed point theorems, and calculus on time scales we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for that class of neural networks. The results of this paper are completely new and complementary to the previously known results even if the time scale 𝕋=ℝ or ℤ. Moreover, we present illustrative numerical examples to show the feasibility of our results.
url http://dx.doi.org/10.1155/2014/496396
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AT leiwang periodicsolutionsforshuntinginhibitorycellularneuralnetworksofneutraltypewithtimevaryingdelaysintheleakagetermontimescales
AT yufei periodicsolutionsforshuntinginhibitorycellularneuralnetworksofneutraltypewithtimevaryingdelaysintheleakagetermontimescales
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