Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions
In this paper, we consider higher-order Hopfield neural networks (HHNNs) with time-varying delays. Based on the fixed point theorem, Lyapunov functional method, differential inequality techniques, and without assuming the boundedness on the activation functions, we establish sufficient conditio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/99/abstr.html |
| _version_ | 1828787714646867968 |
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| author | Ya Li Fuxing Zhang |
| author_facet | Ya Li Fuxing Zhang |
| author_sort | Ya Li |
| collection | DOAJ |
| description | In this paper, we consider higher-order Hopfield neural networks (HHNNs) with time-varying delays. Based on the fixed point theorem, Lyapunov functional method, differential inequality techniques, and without assuming the boundedness on the activation functions, we establish sufficient conditions for the existence and local exponential stability of the almost periodic solutions. The results of this paper are new and they complement previously known results. |
| first_indexed | 2024-12-12T00:36:44Z |
| format | Article |
| id | doaj.art-b4759b1703ba4945b9f8a151392efa40 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T00:36:44Z |
| publishDate | 2007-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-b4759b1703ba4945b9f8a151392efa402022-12-22T00:44:20ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-07-01200799110Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functionsYa LiFuxing ZhangIn this paper, we consider higher-order Hopfield neural networks (HHNNs) with time-varying delays. Based on the fixed point theorem, Lyapunov functional method, differential inequality techniques, and without assuming the boundedness on the activation functions, we establish sufficient conditions for the existence and local exponential stability of the almost periodic solutions. The results of this paper are new and they complement previously known results.http://ejde.math.txstate.edu/Volumes/2007/99/abstr.htmlHigh-order Hopfield neural networksalmost periodic solutionexponential stabilitytime-varying delays |
| spellingShingle | Ya Li Fuxing Zhang Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions Electronic Journal of Differential Equations High-order Hopfield neural networks almost periodic solution exponential stability time-varying delays |
| title | Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions |
| title_full | Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions |
| title_fullStr | Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions |
| title_full_unstemmed | Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions |
| title_short | Almost periodic solutions for higher-order Hopfield neural networks without bounded activation functions |
| title_sort | almost periodic solutions for higher order hopfield neural networks without bounded activation functions |
| topic | High-order Hopfield neural networks almost periodic solution exponential stability time-varying delays |
| url | http://ejde.math.txstate.edu/Volumes/2007/99/abstr.html |
| work_keys_str_mv | AT yali almostperiodicsolutionsforhigherorderhopfieldneuralnetworkswithoutboundedactivationfunctions AT fuxingzhang almostperiodicsolutionsforhigherorderhopfieldneuralnetworkswithoutboundedactivationfunctions |