Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms

This paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs....

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Main Authors: Wenxue Li, Tianrui Chen, Ke Wang
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/780387
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author Wenxue Li
Tianrui Chen
Ke Wang
author_facet Wenxue Li
Tianrui Chen
Ke Wang
author_sort Wenxue Li
collection DOAJ
description This paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. Two different kinds of sufficient criteria are derived in the form of Lyapunov function and coefficients of the system, respectively. Finally, a numerical example is given to show the effectiveness of the proposed criteria.
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institution Kabale University
issn 1085-3375
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publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-9bf15f1a64534e66bcbb013de1c4dcf72025-02-03T01:22:04ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/780387780387Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion TermsWenxue Li0Tianrui Chen1Ke Wang2Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaThis paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff's Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. Two different kinds of sufficient criteria are derived in the form of Lyapunov function and coefficients of the system, respectively. Finally, a numerical example is given to show the effectiveness of the proposed criteria.http://dx.doi.org/10.1155/2014/780387
spellingShingle Wenxue Li
Tianrui Chen
Ke Wang
Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
Abstract and Applied Analysis
title Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
title_full Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
title_fullStr Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
title_full_unstemmed Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
title_short Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms
title_sort exponential stability of coupled systems on networks with mixed delays and reaction diffusion terms
url http://dx.doi.org/10.1155/2014/780387
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AT tianruichen exponentialstabilityofcoupledsystemsonnetworkswithmixeddelaysandreactiondiffusionterms
AT kewang exponentialstabilityofcoupledsystemsonnetworkswithmixeddelaysandreactiondiffusionterms