Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/403873 |
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| _version_ | 1850221570973237248 |
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| author | Qiming Liu Rui Xu Zhiping Wang |
| author_facet | Qiming Liu Rui Xu Zhiping Wang |
| author_sort | Qiming Liu |
| collection | DOAJ |
| description | A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results. |
| format | Article |
| id | doaj-art-682cd497494742e8bb589a0f1b24f8d1 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-682cd497494742e8bb589a0f1b24f8d12025-08-20T02:06:41ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/403873403873Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with DelaysQiming Liu0Rui Xu1Zhiping Wang2Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results.http://dx.doi.org/10.1155/2011/403873 |
| spellingShingle | Qiming Liu Rui Xu Zhiping Wang Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays Discrete Dynamics in Nature and Society |
| title | Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays |
| title_full | Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays |
| title_fullStr | Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays |
| title_full_unstemmed | Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays |
| title_short | Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays |
| title_sort | stability and bifurcation of a class of discrete time cohen grossberg neural networks with delays |
| url | http://dx.doi.org/10.1155/2011/403873 |
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