Criterion for Unbounded Synchronous Region in Complex Networks
Synchronization of complex networks has been extensively studied in many fields, where intensive efforts have been devoted to the understanding of its mechanisms. As for discriminating network synchronizability by Master Stability Function method, a dilemma usually encountered is that we have no pri...
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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/10.1155/2013/513871 |
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| _version_ | 1832551398514884608 |
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| author | Jin Zhou |
| author_facet | Jin Zhou |
| author_sort | Jin Zhou |
| collection | DOAJ |
| description | Synchronization of complex networks has been extensively studied in many fields, where intensive efforts have been devoted to the understanding of its mechanisms. As for discriminating network synchronizability by Master Stability Function method, a dilemma usually encountered is that we have no prior knowledge of the network type that the synchronous region belongs to. In this paper, we investigate a sufficient condition for a general complex dynamical network in the absence of control. A main result is that, when the coupling strength is sufficiently strong, the dynamical network achieves synchronization provided that the symmetric part of the inner-coupling matrix is positive definite. According to our results, synchronous region of the network with positive definite inner-coupling matrix belongs to the unbounded one, and then the eigenvalue of the outer-coupling matrix nearest 0 can be used for judging synchronizability. Even though we cannot gain the necessary and sufficient conditions for synchronizing a network so far, our results constitute a first step toward a better understanding of network synchronization. |
| format | Article |
| id | doaj-art-6edc7e83336148caad540dd5c5f6bb56 |
| 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-6edc7e83336148caad540dd5c5f6bb562025-02-03T06:01:35ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/513871513871Criterion for Unbounded Synchronous Region in Complex NetworksJin Zhou0School of Mathematics and Statistics, State Key Lab of Software Engineering, Wuhan University, Wuhan 430072, ChinaSynchronization of complex networks has been extensively studied in many fields, where intensive efforts have been devoted to the understanding of its mechanisms. As for discriminating network synchronizability by Master Stability Function method, a dilemma usually encountered is that we have no prior knowledge of the network type that the synchronous region belongs to. In this paper, we investigate a sufficient condition for a general complex dynamical network in the absence of control. A main result is that, when the coupling strength is sufficiently strong, the dynamical network achieves synchronization provided that the symmetric part of the inner-coupling matrix is positive definite. According to our results, synchronous region of the network with positive definite inner-coupling matrix belongs to the unbounded one, and then the eigenvalue of the outer-coupling matrix nearest 0 can be used for judging synchronizability. Even though we cannot gain the necessary and sufficient conditions for synchronizing a network so far, our results constitute a first step toward a better understanding of network synchronization.http://dx.doi.org/10.1155/2013/513871 |
| spellingShingle | Jin Zhou Criterion for Unbounded Synchronous Region in Complex Networks Abstract and Applied Analysis |
| title | Criterion for Unbounded Synchronous Region in Complex Networks |
| title_full | Criterion for Unbounded Synchronous Region in Complex Networks |
| title_fullStr | Criterion for Unbounded Synchronous Region in Complex Networks |
| title_full_unstemmed | Criterion for Unbounded Synchronous Region in Complex Networks |
| title_short | Criterion for Unbounded Synchronous Region in Complex Networks |
| title_sort | criterion for unbounded synchronous region in complex networks |
| url | http://dx.doi.org/10.1155/2013/513871 |
| work_keys_str_mv | AT jinzhou criterionforunboundedsynchronousregionincomplexnetworks |