Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays
We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stabil...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/805846 |
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| author | Kaiyu Liu Zhengqiu Zhang Liping Wang |
| author_facet | Kaiyu Liu Zhengqiu Zhang Liping Wang |
| author_sort | Kaiyu Liu |
| collection | DOAJ |
| description | We investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous. |
| format | Article |
| id | doaj-art-98bc8ae937b84de79efa8731b8cac5a9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-98bc8ae937b84de79efa8731b8cac5a92025-02-03T05:55:16ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/805846805846Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying DelaysKaiyu Liu0Zhengqiu Zhang1Liping Wang2College of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha 410082, ChinaWe investigate first the existence of periodic solution in general Cohen-Grossberg BAM neural networks with multiple time-varying delays by means of using degree theory. Then using the existence result of periodic solution and constructing a Lyapunov functional, we discuss global exponential stability of periodic solution for the above neural networks. Our result on global exponential stability of periodic solution is different from the existing results. In our result, the hypothesis for monotonicity ineqiality conditions in the works of Xia (2010) Chen and Cao (2007) on the behaved functions is removed and the assumption for boundedness in the works of Zhang et al. (2011) and Li et al. (2009) is also removed. We just require that the behaved functions satisfy sign conditions and activation functions are globally Lipschitz continuous.http://dx.doi.org/10.1155/2012/805846 |
| spellingShingle | Kaiyu Liu Zhengqiu Zhang Liping Wang Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays Abstract and Applied Analysis |
| title | Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays |
| title_full | Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays |
| title_fullStr | Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays |
| title_full_unstemmed | Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays |
| title_short | Existence and Global Exponential Stability of Periodic Solution to Cohen-Grossberg BAM Neural Networks with Time-Varying Delays |
| title_sort | existence and global exponential stability of periodic solution to cohen grossberg bam neural networks with time varying delays |
| url | http://dx.doi.org/10.1155/2012/805846 |
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