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Coordinate transformation and matrix measure approach for synchronization of complex networks
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10.1063/1.3212941
/content/aip/journal/chaos/19/3/10.1063/1.3212941
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/3/10.1063/1.3212941

Figures

Image of FIG. 1.
FIG. 1.

The matrix measures of and , with being given in Eq. (11) and are, respectively, represented by the solid line and the dotted lines above. Lines for , are coincided since is circular for all .

Image of FIG. 2.
FIG. 2.

The matrix measures of and , with given in Eq. (13) and are, respectively, represented by the solid line and the dotted lines above.

Image of FIG. 3.
FIG. 3.

The matrix measures of and , with being given in Eq. (15) and are, respectively, represented by the solid line and the dotted lines above.

Image of FIG. 4.
FIG. 4.

Coupling topologies: (a) generalized wheel-typed coupled network with and (b) prism-typed coupled network with . Networks (a) and (b) appear in Examples 6 and 7, respectively.

Image of FIG. 5.
FIG. 5.

The difference of components of the first two coupled oscillators: (a) the -component partial-state coupling addressed in Case 1 and (b) the -component partial-state coupling addressed in Case 2. In both cases and the outer coupling matrix is given as in Eq. (9).

Image of FIG. 6.
FIG. 6.

The difference of components of the first two coupled oscillators considered in Case 4. Here the -component partial-state coupling is considered with and the outer coupling matrix given as in Eq. (15).

Tables

Generic image for table
Table I.

The table gives the matrix measures of , with various size of , which is given in Eq. (9). Since is a circular matrix, the matrix measures of with respect to and are equal. Note that the matrix measure of is , , which is negative regardless of the size of .

Generic image for table
Table II.

The table gives the matrix measures of , with various size of , which is given in Example 3.

Generic image for table
Table III.

The table gives the matrix measures of , and , with various size of , which is given in Eq. (18).

Generic image for table
Table IV.

The table gives the matrix measures of , and , with various size of , which is given in Example 7.

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/content/aip/journal/chaos/19/3/10.1063/1.3212941
2009-09-08
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Coordinate transformation and matrix measure approach for synchronization of complex networks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/3/10.1063/1.3212941
10.1063/1.3212941
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