Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory
This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. Howe...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/6292597 |
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| _version_ | 1832552038535266304 |
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| author | Ruofeng Rao Shouming Zhong |
| author_facet | Ruofeng Rao Shouming Zhong |
| author_sort | Ruofeng Rao |
| collection | DOAJ |
| description | This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods. |
| format | Article |
| id | doaj-art-b4d427a7750c475da71445483d5c6d3e |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b4d427a7750c475da71445483d5c6d3e2025-02-03T05:59:42ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/62925976292597Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point TheoryRuofeng Rao0Shouming Zhong1Department of Mathematics, Chengdu Normal University, Chengdu 61130, ChinaCollege of Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, ChinaThis paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.http://dx.doi.org/10.1155/2017/6292597 |
| spellingShingle | Ruofeng Rao Shouming Zhong Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory Complexity |
| title | Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory |
| title_full | Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory |
| title_fullStr | Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory |
| title_full_unstemmed | Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory |
| title_short | Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory |
| title_sort | stability analysis of impulsive stochastic reaction diffusion cellular neural network with distributed delay via fixed point theory |
| url | http://dx.doi.org/10.1155/2017/6292597 |
| work_keys_str_mv | AT ruofengrao stabilityanalysisofimpulsivestochasticreactiondiffusioncellularneuralnetworkwithdistributeddelayviafixedpointtheory AT shoumingzhong stabilityanalysisofimpulsivestochasticreactiondiffusioncellularneuralnetworkwithdistributeddelayviafixedpointtheory |