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Onset of synchronization in weighted complex networks: The effect of weight-degree correlation
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10.1063/1.3597646
/content/aip/journal/chaos/21/2/10.1063/1.3597646
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3597646
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Under the WDC scheme, the variation of the synchronization order parameter, , as a function of the coupling strength, ɛ, for different weight parameters, α. The network is generated by the standard BA model (scale-free network), which has size N = 6400 and average degree . Onset of synchronization is identified as the coupling strength where starts to increase from 2 × 10−2. The error bars are estimated by the standard deviation. Each data is averaged over 20 network runs.

Image of FIG. 2.
FIG. 2.

(Color online) Under the WDU scheme, the variations of the synchronization order parameter, , as a function of the coupling strength, ɛ, for scale-free networks (a) and (c) and small-world networks (b). As a reference, the synchronization of non-weighted network (Binary) is also plotted in each subplot. All the networks have size N = 6400 and average degree 6. In constructing the WDU network, each link is arranged a weight chosen randomly from the range [1,100] for (a) and (b), and from the range [1,100000] for (c). The rewiring probability in generating the small-world networks is . The error bars are estimated by the standard deviation, and each data is averaged over 20 network runs.

Image of FIG. 3.
FIG. 3.

(Color online) For the same scale-free network as used in Fig. 1, under WDC weighting scheme, the variation of the critical coupling strength, , as a function of the weight parameter, α, in (a) and the average network gradient, , in (b). Inset: versus α. Each data is averaged over 20 network runs.

Image of FIG. 4.
FIG. 4.

(Color online) For the same scale-free network as used in Fig. 2(a), under WDU scheme, the variation of the critical coupling strength, , as a function of the weight parameter, β, in (a) and the averaged network gradient, , in (b). Insets: versus β. Each data is averaged over 20 network runs.

Image of FIG. 5.
FIG. 5.

(Color online) For the same small-world network as used in Fig. 2(b), under WDU scheme, the variation of the critical coupling strength, , as a function of the weight parameter, β, in (a) and the average network gradient, , in (b). Insets: versus β. Each data is averaged over 20 network runs.

Image of FIG. 6.
FIG. 6.

(Color online) A schematic plot on the distribution of the gradient couplings in WDC and WDU networks. (a) The simplified model of undirected, non-weighted network. (b) The distribution of the gradient couplings under the WDC-scheme. The network nodes and the gradient couplings are organized into a spanned gradient tree, in which each node is reachable from the rooting node (numbered 1). (c) The distribution of the gradient couplings under the WDU-scheme, in which the weight on the link between nodes 3 and 4 is increased by Δ, while the remaining gradients keep identical to that of (b). As Δ exceeds some critical value, the gradient between the nodes 2 and 3 will switch its direction (the red arrow-line), manifesting a breaking of the gradient network. Dashed lines are links dominated by symmetric couplings (with negligible gradient).

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/content/aip/journal/chaos/21/2/10.1063/1.3597646
2011-06-28
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Onset of synchronization in weighted complex networks: The effect of weight-degree correlation
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/2/10.1063/1.3597646
10.1063/1.3597646
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