1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Hierarchical synchronization in complex networks with heterogeneous degrees
Rent:
Rent this article for
USD
10.1063/1.2150381
/content/aip/journal/chaos/16/1/10.1063/1.2150381
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/1/10.1063/1.2150381
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Chaotic attractors of the Rössler oscillator in the phase coherent regime (a) and phase noncoherent regime (b).

Image of FIG. 2.
FIG. 2.

Degree sequence of a SFN with nodes. The inset shows the power-law distribution , averaged over 50 realizations of the networks. The flat tail results from finite size effects.

Image of FIG. 3.
FIG. 3.

Transition to CS in the SFN and the HN, indicated by the synchronization error (squares) and the amplitude of the mean field (circles). The filled symbols are for the SFNs and the open symbols for the HNs. (a) Phase coherent oscillations at . (b) Phase noncoherent oscillations at . In both networks, and .

Image of FIG. 4.
FIG. 4.

Synchronization difference of the oscillators with respect to the global mean field in the SFN (solid line) and HN (dotted line). The symbol (엯) denotes the degree of the nodes. Note the log-log scales of the plots. (a) When the coupling strength is weak and (b) when the synchronized state is perturbed by noise . Here the oscillations are phase noncoherent at and the behavior is very similar for phase coherent oscillations at .

Image of FIG. 5.
FIG. 5.

The average values as a function of at various coupling strength in the SFN. (a) Phase coherent regime . (b) Phase noncoherent regime . The solid line with slop is plotted for reference.

Image of FIG. 6.
FIG. 6.

The average values as a function of in the SFN at various noise levels . (a) Phase coherent regime with the coupling strength in the CS region. (b) Phase noncoherent regime with . The solid line with slop is plotted for reference.

Image of FIG. 7.
FIG. 7.

The effective synchronization clusters in the synchronized network in the presence of noise ( , , and ), represented simultaneously in the index space [(a), (b)] and in the degree space [(c), (d)]. A dot is plotted when . (a) and (c) for the threshold value , and (b) and (d) for . The solid lines in (a) and (b) denote and are also plotted in (c) and (d) correspondingly. Note the different scales in (a) and (b) and the log-log scales in (c) and (d).

Image of FIG. 8.
FIG. 8.

as a function of for networks with different degree distributions (power law and exponential) due to different aging exponents . The results obtained in the synchronization regime perturbed by noise ( , , and ) in these different networks collapse into a single curve.

Image of FIG. 9.
FIG. 9.

The amplitude of the mean field as a function of the coupling strength in the SFN (엯) and HN (◻). The solid line is the analytically obtained results [Eq. (20) ] for globally coupled oscillators. The networks have the same mean degree and size .

Image of FIG. 10.
FIG. 10.

(a) Synchronization difference of the oscillators with respect to the global mean field in the SFN (solid line) and HN (dotted line). (b) The average values as a function of in the SFN. (c) and (d), as in (a) and (b), but for the oscillation amplitude and the average value of the oscillators. The results are averaged over 50 realizations of the random time-scale parameters . The coupling strength is .

Image of FIG. 11.
FIG. 11.

The mean oscillation frequencies of the oscillators in the SFN (a) and the HN (b) at the coupling strength .

Image of FIG. 12.
FIG. 12.

Time series of the mean field in the SFN (a) and HN (b) at the coupling strength .

Image of FIG. 13.
FIG. 13.

(a) Phase synchronization order parameter of node with respect to the mean field in the SFN (solid line) and HN (dotted line). (b) Average value of nodes with degree as a function of in the heterogeneous network. (c),(d) as (a) and (b), but for the distance and its average value , respectively. The results are averaged over 50 realizations of random distribution of the time-scale parameter . The coupling strength is .

Image of FIG. 14.
FIG. 14.

(a) Averaged phase difference between a node and the mean field in the SFN (solid line) and HN (dotted line). (b) Average value of nodes with degree as a function of in the SFN. (c),(d) as (a) and (b), but for the absolute difference and its average value , respectively. The solid line in (d) with slope are plotted for reference. The results are averaged over 50 realizations of the random time scale parameters . The coupling strength is .

Image of FIG. 15.
FIG. 15.

Bifurcation diagram of the collective oscillations with respect to the coupling strength . The dots plotted are the local maxima in the time series of . (a) SFN, (b) HN, and (c) Macroscopic equations in Eq. (20) .

Loading

Article metrics loading...

/content/aip/journal/chaos/16/1/10.1063/1.2150381
2006-03-31
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hierarchical synchronization in complex networks with heterogeneous degrees
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/1/10.1063/1.2150381
10.1063/1.2150381
SEARCH_EXPAND_ITEM