Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions
A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existe...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/917835 |
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| _version_ | 1849690462072340480 |
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| author | Yanke Du Yanlu Li Rui Xu |
| author_facet | Yanke Du Yanlu Li Rui Xu |
| author_sort | Yanke Du |
| collection | DOAJ |
| description | A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure that n-dimensional Cohen-Grossberg neural networks with k-level discontinuous activation functions can have kn equilibrium points or kn periodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results. |
| format | Article |
| id | doaj-art-ebe9b7ad06ac4024a3f8e881137a89c5 |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-ebe9b7ad06ac4024a3f8e881137a89c52025-08-20T03:21:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/917835917835Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation FunctionsYanke Du0Yanlu Li1Rui Xu2Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaTraining Department, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaInstitute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, ChinaA general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure that n-dimensional Cohen-Grossberg neural networks with k-level discontinuous activation functions can have kn equilibrium points or kn periodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.http://dx.doi.org/10.1155/2013/917835 |
| spellingShingle | Yanke Du Yanlu Li Rui Xu Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions Discrete Dynamics in Nature and Society |
| title | Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_full | Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_fullStr | Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_full_unstemmed | Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_short | Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions |
| title_sort | multistability and multiperiodicity for a general class of delayed cohen grossberg neural networks with discontinuous activation functions |
| url | http://dx.doi.org/10.1155/2013/917835 |
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