Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium...
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| Main Authors: | , |
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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/10.1155/2012/109319 |
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| _version_ | 1849402748295970816 |
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| author | Yanyan Wang Jianping Zhou |
| author_facet | Yanyan Wang Jianping Zhou |
| author_sort | Yanyan Wang |
| collection | DOAJ |
| description | Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results. |
| format | Article |
| id | doaj-art-943bdcfdb1764f26908e1d6f2ae49daa |
| 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-943bdcfdb1764f26908e1d6f2ae49daa2025-08-20T03:37:28ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/109319109319Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation FunctionsYanyan Wang0Jianping Zhou1School of Mathematics and Physics, Anhui University of Technology, Ma'anshan 243002, ChinaSchool of Computer Science, Anhui University of Technology, Ma'anshan 243002, ChinaCohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property of M-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.http://dx.doi.org/10.1155/2012/109319 |
| spellingShingle | Yanyan Wang Jianping Zhou Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions Abstract and Applied Analysis |
| title | Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_full | Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_fullStr | Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_full_unstemmed | Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_short | Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_sort | global convergence for cohen grossberg neural networks with discontinuous activation functions |
| url | http://dx.doi.org/10.1155/2012/109319 |
| work_keys_str_mv | AT yanyanwang globalconvergenceforcohengrossbergneuralnetworkswithdiscontinuousactivationfunctions AT jianpingzhou globalconvergenceforcohengrossbergneuralnetworkswithdiscontinuousactivationfunctions |