Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays
Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtain...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/570295 |
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| _version_ | 1832558823222542336 |
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| author | Chuangxia Huang Xinsong Yang Yigang He Lehua Huang |
| author_facet | Chuangxia Huang Xinsong Yang Yigang He Lehua Huang |
| author_sort | Chuangxia Huang |
| collection | DOAJ |
| description | Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results. |
| format | Article |
| id | doaj-art-b2f3147010d049629e222440e28bfe86 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b2f3147010d049629e222440e28bfe862025-02-03T01:31:28ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/570295570295Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed DelaysChuangxia Huang0Xinsong Yang1Yigang He2Lehua Huang3College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, ChinaDepartment of Mathematics, Honghe University, Mengzi, Yunnan 661100, ChinaCollege of Electrical and Information Engineering, Hunan University, Changsha, Hunan 410082, ChinaCollege of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410076, ChinaStability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.http://dx.doi.org/10.1155/2011/570295 |
| spellingShingle | Chuangxia Huang Xinsong Yang Yigang He Lehua Huang Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays Discrete Dynamics in Nature and Society |
| title | Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays |
| title_full | Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays |
| title_fullStr | Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays |
| title_full_unstemmed | Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays |
| title_short | Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays |
| title_sort | stability of stochastic reaction diffusion recurrent neural networks with unbounded distributed delays |
| url | http://dx.doi.org/10.1155/2011/570295 |
| work_keys_str_mv | AT chuangxiahuang stabilityofstochasticreactiondiffusionrecurrentneuralnetworkswithunboundeddistributeddelays AT xinsongyang stabilityofstochasticreactiondiffusionrecurrentneuralnetworkswithunboundeddistributeddelays AT yiganghe stabilityofstochasticreactiondiffusionrecurrentneuralnetworkswithunboundeddistributeddelays AT lehuahuang stabilityofstochasticreactiondiffusionrecurrentneuralnetworkswithunboundeddistributeddelays |