Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays
This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summ...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/501891 |
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| author | Yutian Zhang |
| author_facet | Yutian Zhang |
| author_sort | Yutian Zhang |
| collection | DOAJ |
| description | This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stability of the equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction-diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results. |
| format | Article |
| id | doaj-art-e2534437efe847b29a7010a707453194 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e2534437efe847b29a7010a7074531942025-02-03T01:12:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/501891501891Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying DelaysYutian Zhang0College of Mathematics & Physics, Nanjing University of Information Science & Technology, Nanjing 21004, ChinaThis work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stability of the equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and showed to be dependent on all of the reaction-diffusion coefficients, the dimension of the space, the delay, and the boundary of the spatial variables. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.http://dx.doi.org/10.1155/2012/501891 |
| spellingShingle | Yutian Zhang Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays Journal of Applied Mathematics |
| title | Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays |
| title_full | Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays |
| title_fullStr | Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays |
| title_full_unstemmed | Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays |
| title_short | Asymptotic Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays |
| title_sort | asymptotic stability of impulsive reaction diffusion cellular neural networks with time varying delays |
| url | http://dx.doi.org/10.1155/2012/501891 |
| work_keys_str_mv | AT yutianzhang asymptoticstabilityofimpulsivereactiondiffusioncellularneuralnetworkswithtimevaryingdelays |