Globally Exponential Synchronization and Synchronizability for General Dynamical Networks
The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient ev...
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| Veröffentlicht in: | IEEE transactions on cybernetics 2010-04, Vol.40 (2), p.350-361 |
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| creator | Jianquan Lu Ho, D.W.C. |
| description | The globally exponential synchronization problem for general dynamical networks is considered in this paper. One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks. |
| doi_str_mv | 10.1109/TSMCB.2009.2023509 |
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One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. 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One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.</description><subject>Asymmetric</subject><subject>Asymmetry</subject><subject>Biology</subject><subject>Chaotic communication</subject><subject>Complex networks</subject><subject>Criteria</subject><subject>Cybernetics</subject><subject>Differential equations</subject><subject>Dynamical systems</subject><subject>Image storage</subject><subject>Joining</subject><subject>large-scale dynamical networks</subject><subject>Large-scale systems</subject><subject>Mathematics</subject><subject>Network topology</subject><subject>Networks</subject><subject>reducible</subject><subject>Sociology</subject><subject>Spatiotemporal phenomena</subject><subject>Synchronism</subject><subject>synchronizability</subject><subject>Synchronization</subject><issn>1083-4419</issn><issn>2168-2267</issn><issn>1941-0492</issn><issn>2168-2275</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kU1v1DAQhi0Eoh_wB0BCkTiUS8qM7cSZIyxlQSpwaDlwipxkIlyy9mJnBeHX47IrQBy42CPP8441eoR4hHCOCPT8-urd6uW5BKB8SFUB3RHHSBpL0CTv5hoaVWqNdCROUrqBTAKZ--IIqakakM2x-LSeQmenaSkuvm-DZz87OxVXi-8_x-DdDzu74Avrh7_fOje5eSnGEIs1e4458WrxduP6XL3n-VuIX9IDcW-0U-KHh_tUfHx9cb16U15-WL9dvbgse9WouVRm6ABRW6p5NMb0miUSA9Noq64fqKLaotIKaiLFPA5c13rAAZRRbEidirP93G0MX3ec5nbjUs_TZD2HXWqN0qDyD5DJZ_8lsTaooJJ1ldGn_6A3YRd93qNFkAZ1paXMlNxTfQwpRR7bbXQbG5cMtbeK2l-K2ltF7UFRDj05jN51Gx7-RA5OMvB4Dzhm_t2uJKFpUP0EsnCVFg</recordid><startdate>201004</startdate><enddate>201004</enddate><creator>Jianquan Lu</creator><creator>Ho, D.W.C.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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One quantity will be distilled from the coupling matrix to characterize the synchronizability of the corresponding dynamical networks. The calculation of such a quantity is very convenient even for large-scale networks. The network topology is assumed to be directed and weakly connected, which implies that the coupling configuration matrix can be asymmetric, weighted, or reducible. This assumption is more consistent with the realistic network in practice than the constraint of symmetry and irreducibility. By using the Lyapunov functional method and the Kronecker product techniques, some criteria are obtained to guarantee the globally exponential synchronization of general dynamical networks. In addition, numerical examples, including small-world and scale-free networks, are given to demonstrate the theoretical results. It will be shown that our criteria are available for large-scale dynamical networks.</abstract><cop>United States</cop><pub>IEEE</pub><pmid>19858028</pmid><doi>10.1109/TSMCB.2009.2023509</doi><tpages>12</tpages></addata></record> |
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| subjects | Asymmetric Asymmetry Biology Chaotic communication Complex networks Criteria Cybernetics Differential equations Dynamical systems Image storage Joining large-scale dynamical networks Large-scale systems Mathematics Network topology Networks reducible Sociology Spatiotemporal phenomena Synchronism synchronizability Synchronization |
| title | Globally Exponential Synchronization and Synchronizability for General Dynamical Networks |
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