Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency
This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a nove...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/402031 |
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| _version_ | 1832556104635121664 |
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| author | Xinsong Yang Mengzhe Zhou Jinde Cao |
| author_facet | Xinsong Yang Mengzhe Zhou Jinde Cao |
| author_sort | Xinsong Yang |
| collection | DOAJ |
| description | This paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-12c91c42e30741948ede797aa5b516af |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-12c91c42e30741948ede797aa5b516af2025-02-03T05:46:21ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/402031402031Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission EfficiencyXinsong Yang0Mengzhe Zhou1Jinde Cao2Department of Mathematics, Chongqing Normal University, Chongqing 400047, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaThis paper investigates global synchronization in an array of coupled neural networks with time-varying delays and unbounded distributed delays. In the coupled neural networks, limited transmission efficiency between coupled nodes, which makes the model more practical, is considered. Based on a novel integral inequality and the Lyapunov functional method, sufficient synchronization criteria are derived. The derived synchronization criteria are formulated by linear matrix inequalities (LMIs) and can be easily verified by using Matlab LMI Toolbox. It is displayed that, when some of the transmission efficiencies are limited, the dynamics of the synchronized state are different from those of the isolated node. Furthermore, the transmission efficiency and inner coupling matrices between nodes play important roles in the final synchronized state. The derivative of the time-varying delay can be any given value, and the time-varying delay can be unbounded. The outer-coupling matrices can be symmetric or asymmetric. Numerical simulations are finally given to demonstrate the effectiveness of the theoretical results.http://dx.doi.org/10.1155/2013/402031 |
| spellingShingle | Xinsong Yang Mengzhe Zhou Jinde Cao Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency Abstract and Applied Analysis |
| title | Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency |
| title_full | Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency |
| title_fullStr | Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency |
| title_full_unstemmed | Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency |
| title_short | Synchronization in Array of Coupled Neural Networks with Unbounded Distributed Delay and Limited Transmission Efficiency |
| title_sort | synchronization in array of coupled neural networks with unbounded distributed delay and limited transmission efficiency |
| url | http://dx.doi.org/10.1155/2013/402031 |
| work_keys_str_mv | AT xinsongyang synchronizationinarrayofcoupledneuralnetworkswithunboundeddistributeddelayandlimitedtransmissionefficiency AT mengzhezhou synchronizationinarrayofcoupledneuralnetworkswithunboundeddistributeddelayandlimitedtransmissionefficiency AT jindecao synchronizationinarrayofcoupledneuralnetworkswithunboundeddistributeddelayandlimitedtransmissionefficiency |