Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings
We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. Inspired by our previous paper (Lu et al. (2007-2008)), the extended H...
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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/10.1155/2013/134265 |
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| _version_ | 1832567689009168384 |
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| author | Xinlei Yi Wenlian Lu Tianping Chen |
| author_facet | Xinlei Yi Wenlian Lu Tianping Chen |
| author_sort | Xinlei Yi |
| collection | DOAJ |
| description | We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. Inspired by our previous paper (Lu et al. (2007-2008)), the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness of the theoretical results. |
| format | Article |
| id | doaj-art-d46c08721cc642dca966bb0841fd05f0 |
| 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-d46c08721cc642dca966bb0841fd05f02025-02-03T01:00:53ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/134265134265Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying CouplingsXinlei Yi0Wenlian Lu1Tianping Chen2School of Mathematical Sciences, Fudan University, Shanghai 200433, ChinaSchool of Mathematical Sciences, Fudan University, Shanghai 200433, ChinaSchool of Mathematical Sciences, Fudan University, Shanghai 200433, ChinaWe study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. Inspired by our previous paper (Lu et al. (2007-2008)), the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness of the theoretical results.http://dx.doi.org/10.1155/2013/134265 |
| spellingShingle | Xinlei Yi Wenlian Lu Tianping Chen Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings Abstract and Applied Analysis |
| title | Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings |
| title_full | Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings |
| title_fullStr | Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings |
| title_full_unstemmed | Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings |
| title_short | Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings |
| title_sort | achieving synchronization in arrays of coupled differential systems with time varying couplings |
| url | http://dx.doi.org/10.1155/2013/134265 |
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