Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms
This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise suff...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/409758 |
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| _version_ | 1832548685060243456 |
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| author | Jinhua Huang Jiqing Liu Guopeng Zhou |
| author_facet | Jinhua Huang Jiqing Liu Guopeng Zhou |
| author_sort | Jinhua Huang |
| collection | DOAJ |
| description | This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results. |
| format | Article |
| id | doaj-art-855bfe6ea1e1425d86861c718baf110b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-855bfe6ea1e1425d86861c718baf110b2025-02-03T06:13:27ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/409758409758Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion TermsJinhua Huang0Jiqing Liu1Guopeng Zhou2College of Electric and Electronic Engineering, Wuhan Institute of Shipbuilding Technology, Wuhan, Hubei 430050, ChinaCollege of Electric and Electronic Engineering, Wuhan Institute of Shipbuilding Technology, Wuhan, Hubei 430050, ChinaCollege of Electronic and Information Engineering, Hubei University of Science and Technology, Xianning, Hubei 437100, ChinaThis work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.http://dx.doi.org/10.1155/2013/409758 |
| spellingShingle | Jinhua Huang Jiqing Liu Guopeng Zhou Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms Abstract and Applied Analysis |
| title | Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_full | Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_fullStr | Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_full_unstemmed | Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_short | Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms |
| title_sort | stability of impulsive cohen grossberg neural networks with time varying delays and reaction diffusion terms |
| url | http://dx.doi.org/10.1155/2013/409758 |
| work_keys_str_mv | AT jinhuahuang stabilityofimpulsivecohengrossbergneuralnetworkswithtimevaryingdelaysandreactiondiffusionterms AT jiqingliu stabilityofimpulsivecohengrossbergneuralnetworkswithtimevaryingdelaysandreactiondiffusionterms AT guopengzhou stabilityofimpulsivecohengrossbergneuralnetworkswithtimevaryingdelaysandreactiondiffusionterms |