Effective centrality and explosive synchronization in complex networks

Navas, Adrián; Villacorta-Atienza, José Antonio; Leyva, I.; Almendral, Juan A.; Sendiña‐Nadal, Irene; Boccaletti, Stefano

doi:10.1103/physreve.92.062820

Cited by 20 publications

(15 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further properties of synchronization in the presence of correlations between the intrinsic dynamics of the oscillators and their local topology were investigated in [255,274,275] as well as the dynamics in other types of networks, such as in modular [139] and in co-evolving [246] ones. The effects of partially correlating frequencies and degrees were also investigated [256].…”

Section: Other Workmentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

View full text Add to dashboard Cite

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

show abstract

Section: Other Workmentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Therefore, we focused on the complexity C i of the sequence of inter-spike times (t l − t l−1 ) patterns of each neuron. Additionally, in order to quantify the level of synchronization, we count how many neurons fire within the same time window [19]. In order to do this, the total simulation time T is divided in n = 1, .…”

Section: B Stochastic Dynamics: the Morris-lecar Neuronmentioning

confidence: 99%

“…It is well known that, in the path to synchrony, the role of the nodes differs as a result of their various topological positions [16,19] as well as of their own intrinsic dynamics [20]. Thus, the role of the highly connected nodes (hubs) as coordinators of the dynamics of the whole system has been very often considered [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Dynamical complexity as a proxy for the network degree distribution

et al. 2019

Self Cite

View full text Add to dashboard Cite

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the nodes is found to be a function of their topological role, with nodes of higher degree displaying lower levels of complexity. We provide several examples of theoretical models of chaotic oscillators, pulse-coupled neurons and experimental networks of nonlinear electronic circuits evidencing such a hierarchical behavior. Importantly, our results imply that it is possible to infer the degree distribution of a network only from individual dynamical measurements.

show abstract

“…Figure 4 then clarifies that the enhancement of the hysteresis is associated with a moderate increase in the degree-degree correlation, recovering a second-order transition for large values of positive and negative r. This nontrivial effect can be understood by examining the inner mechanism of the frequency-degree correlation. Explosive transitions result from a frustration in the path to synchronization [45], In the case of ER networks, where the path to synchronization starts from multiple seeds homogeneously distributed in the network, this frustration can be induced by imposing a gap in the frequency differences of each pair of nodes. The larger is the gap frequency, the higher is the frustration (explosivity) of the system, which shows a positive correlation between the explosive character of the system and the width of the hysteresis [23].…”

Section: The Effect Of the Degree Mixingmentioning

confidence: 99%

Effects of degree correlations on the explosive synchronization of scale-free networks

et al. 2015

Self Cite

View full text Add to dashboard Cite

We study the organization of finite-size, large ensembles of phase oscillators networking via scale-free topologies in the presence of a positive correlation between the oscillators' natural frequencies and the network's degrees. Under those circumstances, abrupt transitions to synchronization are known to occur in growing scale-free networks, while the transition has a completely different nature for static random configurations preserving the same structure-dynamics correlation. We show that the further presence of degree-degree correlations in the network structure has important consequences on the nature of the phase transition characterizing the passage from the phase-incoherent to the phase-coherent network state. While high levels of positive and negative mixing consistently induce a second-order phase transition, moderate values of assortative mixing, such as those ubiquitously characterizing social networks in the real world, greatly enhance the irreversible nature of explosive synchronization in scale-free networks. The latter effect corresponds to a maximization of the area and of the width of the hysteretic loop that differentiates the forward and backward transitions to synchronization.

show abstract

Effective centrality and explosive synchronization in complex networks

Cited by 20 publications

References 32 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Dynamical complexity as a proxy for the network degree distribution

Effects of degree correlations on the explosive synchronization of scale-free networks

Contact Info

Product

Resources

About