Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes
We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally fo...
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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/10.1155/2013/946243 |
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| _version_ | 1832547496489910272 |
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| author | Ze Tang Jianwen Feng |
| author_facet | Ze Tang Jianwen Feng |
| author_sort | Ze Tang |
| collection | DOAJ |
| description | We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result. |
| format | Article |
| id | doaj-art-388e78df5b8a445ab8f5c9b313c728cd |
| 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-388e78df5b8a445ab8f5c9b313c728cd2025-02-03T06:44:37ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/946243946243Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical NodesZe Tang0Jianwen Feng1College of Mathematics and Computational Sciences, Shenzhen University, Shenzhen, Guangdong 518060, ChinaCollege of Mathematics and Computational Sciences, Shenzhen University, Shenzhen, Guangdong 518060, ChinaWe focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.http://dx.doi.org/10.1155/2013/946243 |
| spellingShingle | Ze Tang Jianwen Feng Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes Abstract and Applied Analysis |
| title | Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes |
| title_full | Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes |
| title_fullStr | Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes |
| title_full_unstemmed | Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes |
| title_short | Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes |
| title_sort | adaptive cluster synchronization for nondelayed and delayed coupling complex networks with nonidentical nodes |
| url | http://dx.doi.org/10.1155/2013/946243 |
| work_keys_str_mv | AT zetang adaptiveclustersynchronizationfornondelayedanddelayedcouplingcomplexnetworkswithnonidenticalnodes AT jianwenfeng adaptiveclustersynchronizationfornondelayedanddelayedcouplingcomplexnetworkswithnonidenticalnodes |