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On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators
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10.1063/1.3590855
/content/aip/journal/chaos/21/2/10.1063/1.3590855
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3590855
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Synchrony order parameter as a function of coupling strength K for the initial random ER network (dashed line, online blue) and for the synchrony optimized version of the same network using the approach detailed in Sec. III (continuous line, online red). The DRA synchrony optimization was performed at .

Image of FIG. 2.
FIG. 2.

(Color online) Change of structural network parameters during the DRA optimization process. The lowest value of refers to the initial random network and the largest value of to the final synchrony optimized network. (a) Average path length , (b) clustering coefficient C, (c) frequency sign ratio , and (d) frequency correlation . We used an initial ER with nodes and , and initialized the DRA optimization at .

Image of FIG. 3.
FIG. 3.

Illustration of networks of minimal energy E. Left: Initial ER with nodes. Nodes with positive frequencies are on the right and nodes with negative frequencies on the left. Nodes are ordered from top to bottom with decreasing absolute value of their frequencies. Right: The same network but rewired to minimize E.

Image of FIG. 4.
FIG. 4.

(Color online) Synchrony order parameter as a function of coupling strength K for optimal networks with nodes and mean degree produced by the dynamic approach (DRA) (continuous line, online red) and by minimizing E (dashed line, online blue). We used an average over six E-minimized networks generated from different initial ER networks with same N and mean degree.

Image of FIG. 5.
FIG. 5.

Sketch of the rewiring. The nodes with negative native frequencies are on the left hand side and the nodes with positive native frequencies on the right hand side.

Image of FIG. 6.
FIG. 6.

(Color online) Visual representation of the adjacency matrix of node -networks for different values of q. Here, we assume the node indices are sorted by decreasing native frequency. Entries with are coloured dark (online blue). Left: E-minimized network with . Middle: . Right: .

Image of FIG. 7.
FIG. 7.

(Color online) Energy E and path length as a function of the rewiring probability q. The red dashed line represents the energy of the E-minimized network.

Image of FIG. 8.
FIG. 8.

(Color online) Log-log plot of the average path length as a function of the rewiring probability q. The slope of the line of best fit (dashed line) is 0.493.

Image of FIG. 9.
FIG. 9.

(Color online) Synchrony order parameter as a function of coupling strength K for the synchrony-optimized networks. We show a DRA-optimized network (continuous line, online red) and several -networks with (dashed, online blue), (crosses, online green), and (triangles, online magenta). For the energy minimized networks with , we have plotted an average over 6 seperate networks.

Image of FIG. 10.
FIG. 10.

(Color online) Left: Synchrony order parameter as a function of the rewiring probability q for several values of the coupling strength K. Right: For the coupling strength , we present a zoom at low values of q showing that there exists a value such that synchronization is maximized.

Image of FIG. 11.
FIG. 11.

(Color online) Order parameter as a function of coupling strength K for the local synchronization branch for the -networks with (continuous line, online blue). The dashed line (online red) shows the best linear fit and the dashed-dotted line (online magenta) shows the predicted linear behaviour [Eq. (4.2)]. For this particular network, . The line of best fit has slope .

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/content/aip/journal/chaos/21/2/10.1063/1.3590855
2011-06-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3590855
10.1063/1.3590855
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