Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales
We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/386706 |
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| _version_ | 1850163526454214656 |
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| author | Yaping Ren Yongkun Li |
| author_facet | Yaping Ren Yongkun Li |
| author_sort | Yaping Ren |
| collection | DOAJ |
| description | We study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of the previously known results. |
| format | Article |
| id | doaj-art-e7f04074648045f7bff6c35a35b84fc9 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e7f04074648045f7bff6c35a35b84fc92025-08-20T02:22:15ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/386706386706Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time ScalesYaping Ren0Yongkun Li1School of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, ChinaDepartment of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaWe study delayed cellular neural networks on time scales. Without assuming the boundedness of the activation functions, we establish the exponential stability and existence of periodic solutions. The results in this paper are completely new even in case of the time scale 𝕋=ℝ or ℤ and improve some of the previously known results.http://dx.doi.org/10.1155/2012/386706 |
| spellingShingle | Yaping Ren Yongkun Li Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales Discrete Dynamics in Nature and Society |
| title | Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales |
| title_full | Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales |
| title_fullStr | Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales |
| title_full_unstemmed | Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales |
| title_short | Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales |
| title_sort | stability and existence of periodic solutions for cellular neural networks with state dependent delays on time scales |
| url | http://dx.doi.org/10.1155/2012/386706 |
| work_keys_str_mv | AT yapingren stabilityandexistenceofperiodicsolutionsforcellularneuralnetworkswithstatedependentdelaysontimescales AT yongkunli stabilityandexistenceofperiodicsolutionsforcellularneuralnetworkswithstatedependentdelaysontimescales |