Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays
This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by usin...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/3826729 |
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| _version_ | 1849692099413278720 |
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| author | Xiaohui Xu Jiye Zhang Quan Xu Zilong Chen Weifan Zheng |
| author_facet | Xiaohui Xu Jiye Zhang Quan Xu Zilong Chen Weifan Zheng |
| author_sort | Xiaohui Xu |
| collection | DOAJ |
| description | This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results. |
| format | Article |
| id | doaj-art-b08d04b8753e4763becd6d8897917f6a |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b08d04b8753e4763becd6d8897917f6a2025-08-20T03:20:50ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/38267293826729Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed DelaysXiaohui Xu0Jiye Zhang1Quan Xu2Zilong Chen3Weifan Zheng4Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu 610039, ChinaNational Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, ChinaSchool of Technology, Xihua University, Chengdu 610039, ChinaKey Laboratory of Automotive Measurement, Control and Safety, Sichuan Province, Xihua University, Chengdu 610039, ChinaInstitute of Information Research, Southwest Jiaotong University, Chengdu 610031, ChinaThis paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.http://dx.doi.org/10.1155/2017/3826729 |
| spellingShingle | Xiaohui Xu Jiye Zhang Quan Xu Zilong Chen Weifan Zheng Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays Complexity |
| title | Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays |
| title_full | Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays |
| title_fullStr | Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays |
| title_full_unstemmed | Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays |
| title_short | Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays |
| title_sort | impulsive disturbances on the dynamical behavior of complex valued cohen grossberg neural networks with both time varying delays and continuously distributed delays |
| url | http://dx.doi.org/10.1155/2017/3826729 |
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