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Evolution of microscopic and mesoscopic synchronized patterns in complex networks
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10.1063/1.3532801
/content/aip/journal/chaos/21/1/10.1063/1.3532801
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/1/10.1063/1.3532801
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Size of the giant synchronized component. We plot here the probability of finding a giant synchronized component of a given size, N sync, for different values of the coupling strength λ. The upper and bottom figures correspond to ER and SF networks, respectively. N = 1000 in both cases. The results for every value of λ are obtained using a sample of 104 different realizations. While for ER networks there is a clear gap in P(N sync), SF networks show a gradual shift to the right without significant jumps in P(N sync) as λ is increased.

Image of FIG. 2.
FIG. 2.

(Color online) Evolution of the size of the GSC when increasing the coupling strength in ER (top) and SF (bottom) networks. To capture the growth of the GSC size as the coupling strength is increased from λ to λ + δλ (with δλ = 0.01), we plot the function N sync(λ + δλ) = f[N sync(λ)]. A total number of 104 numerical continuations have been carried for every value of λ ɛ [0.01, 0.14]. The color of the dots denotes the corresponding value of λ as shown in the color bar.

Image of FIG. 3.
FIG. 3.

(Color online) Number of synchronized links in the giant synchronized component. We plot the probability of finding a giant synchronized component with a given number of links, L sync, for different values of the coupling strength λ. The upper and bottom figures correspond to ER and SF networks, respectively. The distributions are obtained as in Fig. 1.

Image of FIG. 4.
FIG. 4.

(Color online) Number of synchronized links, L sync, after increasing the coupling. Same philosophy as Fig. 2: We construct the map L sync(λ + δλ) = g[L sync(λ)] by following the evolution of the synchronized GSC as the coupling λ is increased from 0.01 to 0.15. The evolution for the ER network (top) shows two big jumps in the number of links incorporated into the GSC in contrast with the continuous shape of g(x) for the SF topology (bottom). Both panels show a number of 104 numerical continuations.

Image of FIG. 5.
FIG. 5.

(Color online) Evolution of the average path length of the GSC along the synchronization path. We show the change in the APL of the GSC of ER (top) and SF (bottom) networks when passing from λ to λ + δλ with δλ = 0.01. In both panels, we plot the relation 〈lsync(λ + δλ) = h[〈lsync(λ)] observed in 104 numerical continuation along the range λ ɛ [0.01, 0.14] . As denoted by the dotted line in the top panel, a sudden decrease of the APL in the GSC of ER networks occurs at λ ≃ 0.12 due to the fast addition of links into the GSC. Such a dramatic change is not observed for SF networks, and the APL gradually decreases as shown by the dotted line.

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/content/aip/journal/chaos/21/1/10.1063/1.3532801
2011-03-29
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Evolution of microscopic and mesoscopic synchronized patterns in complex networks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/1/10.1063/1.3532801
10.1063/1.3532801
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