Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators
We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to en...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/595360 |
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| _version_ | 1849693554063966208 |
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| author | Zhen Jia Guangming Deng |
| author_facet | Zhen Jia Guangming Deng |
| author_sort | Zhen Jia |
| collection | DOAJ |
| description | We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis. |
| format | Article |
| id | doaj-art-2fdebb7d1ab04b869ea14cabcf211001 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2fdebb7d1ab04b869ea14cabcf2110012025-08-20T03:20:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/595360595360Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic OscillatorsZhen Jia0Guangming Deng1College of Science, Guilin University of Technology, Guilin 541004, ChinaCollege of Science, Guilin University of Technology, Guilin 541004, ChinaWe propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. The global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. The cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. Theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. All of the results are proved rigorously. Finally, a network with a scale-free subnetwork and a small-world subnetwork is illustrated, and the corresponding numerical simulations verify the theoretical analysis.http://dx.doi.org/10.1155/2012/595360 |
| spellingShingle | Zhen Jia Guangming Deng Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators Journal of Applied Mathematics |
| title | Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators |
| title_full | Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators |
| title_fullStr | Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators |
| title_full_unstemmed | Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators |
| title_short | Mathematical Model and Cluster Synchronization for a Complex Dynamical Network with Two Types of Chaotic Oscillators |
| title_sort | mathematical model and cluster synchronization for a complex dynamical network with two types of chaotic oscillators |
| url | http://dx.doi.org/10.1155/2012/595360 |
| work_keys_str_mv | AT zhenjia mathematicalmodelandclustersynchronizationforacomplexdynamicalnetworkwithtwotypesofchaoticoscillators AT guangmingdeng mathematicalmodelandclustersynchronizationforacomplexdynamicalnetworkwithtwotypesofchaoticoscillators |