Factors that predict better synchronizability on complex networks

Abstract

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network, the suppressing tendency of the heterogeneity of the degree distribution, even for shorter characteristic path length, has also been reported. To see this, we investigate the effects of various factors such as the degree, characteristic path length, heterogeneity, and betweenness centrality on synchronization, and find a consistent trend between the synchronization and the betweenness centrality. The betweenness centrality is thus proposed as a good indicator for synchronizability.

Network synchronization: Spectral versus statistical properties

“…Since the o(1) term has no bounds in terms of graph size, it need not be small for a large but finite graph. Moreover, to neglect the second term on the right-hand side of (14), it is necessary that the expected minimum degree w min grow faster than log 2 n as n → ∞. In other words, (15) can be justified only for graphs for which both the size and the minimum degree are very large.…”

“…Many recent papers have investigated various facets of this relation. For example, some papers have reported correlations between network synchronizability and degree homogeneity [9][10][11], clustering coefficient [12], degree correlations [13], average degree, degree distribution, and so on [14]. In some cases the observed correlations can point in opposite directions; for instance, [9] finds that increasing the degree homogeneity improves synchronizability, whereas [14] and [13] report cases of better synchronizability for decreased homogeneity.…”

“…For example, some papers have reported correlations between network synchronizability and degree homogeneity [9][10][11], clustering coefficient [12], degree correlations [13], average degree, degree distribution, and so on [14]. In some cases the observed correlations can point in opposite directions; for instance, [9] finds that increasing the degree homogeneity improves synchronizability, whereas [14] and [13] report cases of better synchronizability for decreased homogeneity. Similarly, adding a few shortcut links to a sparse lattice is known to decrease the characteristic path length and improve synchronizability at the same time [15,16], although another study showed that better synchronization can result despite increased average distance [9].…”

Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons

“…The main idea was that the impact of network topology on the global dynamics might be prominent, so that these structural statistics may be good indicators of the global dynamics. This assumption proved however largely wrong so that some of the related studies yielded contradictory results [35,27]. Actually, synchronization properties cannot be systematically deduced from topology statistics but may be inferred from the spectrum of the network [3].…”

Firing Patterns in Coupled Systems of Inhibitory Neurons

“…Barahona and Pecora developed master stability function (MSF) analysis to study synchronizability in complex networks [8], and Nishikawa and Motter extended it for an asymmetric case [9]. Since the average path length becomes short in small-world networks, synchronization is achieved more easily than in a regular lattice [10][11][12][13]. However, this is not the only condition; synchronizability also depends on the network size, the degree distribution (distribution of the number of links), the clustering coefficient, and so forth [14][15][16][17].…”