Enhancing synchronizability of weighted dynamical networks using betweenness centrality (original) (raw)
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Onset of synchronization in weighted complex networks: The effect of weight-degree correlation
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011
By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and node degree is also important to the network dynamics.
Synchronization is Enhanced in Weighted Complex Networks
Physical Review Letters, 2005
The propensity for synchronization of complex networks with directed and weighted links is considered. We show that a weighting procedure based upon the global structure of network pathways enhances complete synchronization of identical dynamical units in scale-free networks. Furthermore, we numerically show that very similar conditions hold also for phase synchronization of nonidentical chaotic oscillators.
Synchronizability determined by coupling strengths and topology on complex networks
Physical Review E, 2007
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also present new details on the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces new parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.
Dynamical Weights and Enhanced Synchronization in Adaptive Complex Networks
Physical Review Letters, 2006
Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks.
Generalized synchronization in mutually coupled oscillators and complex networks
Physical Review E, 2012
We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.
Enhancing synchronization in complex networks of coupled phase oscillators
2007
By a model of coupled phase oscillators, we show analytically how synchronization in non-identical complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from the large-degree to the small-degree nodes on each link, increase of the gradient strength will bring forward the onset of network synchronization monotonically, and, with the same gradient strength, heterogeneous networks are more synchronizable than homogeneous networks. The findings are tested by extensive simulations and good agreement are found.
The development of generalized synchronization on complex networks
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009
In this paper, we investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks and modular networks. By adopting the auxiliary-system approach to networks, we show that GS can take place in oscillator networks with both heterogeneous and homogeneous degree distribution, regardless of whether the coupled chaotic oscillators are identical or nonidentical. For coupled identical oscillators on networks, we find that there exists a general bifurcation path from initial non-synchronization to final global complete synchronization (CS) via GS as the coupling strength is increased. For coupled nonidentical oscillators on networks, we further reveal how network topology competes with the local dynamics to dominate the development of GS on networks. Especially, we analyze how different coupling strategies affect the development of GS on complex networks. Our findings provide a further understanding for the occurrence and development of collective behavior in complex networks.
Factors that predict better synchronizability on complex networks
2004
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.
arXiv (Cornell University), 2021
Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their connectivities change with time, depending on the dynamical state of the system. Networks of adaptively coupled oscillators show various synchronization phenomena, such as hierarchical multifrequency clusters, traveling waves, or chimera states. While these self-organized patterns have been previously studied on all-toall coupled networks, this work extends the investigations towards more complex networks, analyzing the influence of random network topologies for various degrees of dilution of the connectivities. Using numerical and analytical approaches, we investigate the robustness of multicluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against the random dilution of the underlying network topology. Further, we utilize the master stability approach for adaptive networks in order to highlight the interplay between adaptivity and topology.