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Effects of the network structural properties on its controllability
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10.1063/1.2743098
/content/aip/journal/chaos/17/3/10.1063/1.2743098
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/3/10.1063/1.2743098
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Networks of nodes, edges, . and are plotted vs in networks characterized by different degree distribution . The legend is as follows: , (stars); , (diamonds); , (plus); , (circles); , (squares).

Image of FIG. 2.
FIG. 2.

(Color online) A scale-free network of nodes with degree distribution exponent is considered. The figure shows the eigenratio as varying both the control gain with and the number of controlled nodes (in terms of the probability ).

Image of FIG. 3.
FIG. 3.

(Color online) Control error at regime as a function of the control gain with and the probability under the same conditions as in Fig. 2 .

Image of FIG. 4.
FIG. 4.

(Color online) A scale-free network of nodes with degree distribution exponent is considered. The figure shows the eigenratio as varying both the control gain with and the number of controlled nodes (in terms of the probability ).

Image of FIG. 5.
FIG. 5.

(Color online) Control error at regime as a function of the control gain with and the probability under the same conditions as in Fig. 4 .

Image of FIG. 6.
FIG. 6.

(Color online) Networks of nodes. The controllability is plotted vs the number of controlled nodes for networks characterized by different degree distribution exponents: in (a), in (b), in (c), in (d). Black (red) is used for random (selective) pinning. Different lines represent different values of the control gain , ranging from to .

Image of FIG. 7.
FIG. 7.

(Color online) Random pinning of networks characterized by different degree correlation properties, , , . Here we consider a scale-free heterogeneous network with degree distribution exponent . The controllability is reported vs the number of controlled nodes , by having in each picture a different value of the control gain : (a) , (b) , (c) , (d) , (e) , (f) . Different degree correlation properties are indicated by different symbols: Triangles are used in the case of assortative networks , squares in the case of disassortative networks , and circles in the case of networks that do not display degree correlation .

Image of FIG. 8.
FIG. 8.

(Color online) Selective pinning of networks characterized by different degree correlation properties, , , . Here we consider a scale-free heterogeneous network with degree distribution exponent . The controllability is reported vs the number of controlled nodes , by having in each picture a different value of the control gain : (a) , (b) , (c) , (d) , (e) , (f) . Different degree correlation properties are indicated by different symbols: Triangles are used in the case of assortative networks , squares in the case of disassortative networks , and circles in the case of networks that do not display degree correlation .

Image of FIG. 9.
FIG. 9.

A monodimensional lattice of nodes is considered. The controllability indices and are plotted as functions of the control gain . The legend is as follows: (circles), (triangles), (stars), (diamonds), and (plus).

Image of FIG. 10.
FIG. 10.

A monodimensional lattice of nodes is considered. Assuming that the controlled nodes are node 1 and node , the controllability indices and are plotted vs . Different lines indicate different control gains : (asterisks), (circles), (no marker), and (dots).

Image of FIG. 11.
FIG. 11.

A periodic square lattice of nodes is considered. The controllability indices and are plotted as functions of the control gain . The legend is as follows: (circles), (triangles), (stars), (diamonds), and (plus).

Image of FIG. 12.
FIG. 12.

A square lattice of nodes is considered. Assuming that two of its nodes have been chosen to be controlled, the controllability indices and are plotted vs their distance . Different lines indicate different control gains : (asterisks), (circles), (no marker), and (dots).

Image of FIG. 13.
FIG. 13.

(Color online) A random network of nodes composed of two communities is considered. The first one, , includes 125 nodes and the second one, , includes the remaining (375) ones. The network controllability is plotted vs in (a) and (b) [(c) and (d)] as is varied between 1 and 0, according to the technique described in the text. The pinning probability is assumed to be . Different lines indicate several values of the control gain : (points), (no marker), (squares), (diamonds), (times), and (asterisks). The left plots (a) and (c) show the cases in which the controllers are evenly distributed among the two communities. The right plots (b) and (d) show a situation in which 95% of the controllers belong to and the rest to . Observe the logarithmic scale on the axis.

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/content/aip/journal/chaos/17/3/10.1063/1.2743098
2007-07-20
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effects of the network structural properties on its controllability
http://aip.metastore.ingenta.com/content/aip/journal/chaos/17/3/10.1063/1.2743098
10.1063/1.2743098
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