2,014 research outputs found
Synchronization Properties of Network Motifs
We address the problem of understanding the variable abundance of 3-node and
4-node subgraphs (motifs) in complex networks from a dynamical point of view.
As a criterion in the determination of the functional significance of a n-node
subgraph, we propose an analytic method to measure the stability of the
synchronous state (SSS) the subgraph displays. We show that, for undirected
graphs, the SSS is correlated with the relative abundance, while in directed
graphs the correlation exists only for some specific motifs.Comment: 7 pages, 3 figure
Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks
Many real-world networks exhibit degree-assortativity, with nodes of similar
degree more likely to link to one another. Particularly in social networks, the
contribution to the total assortativity varies with degree, featuring a
distinctive peak slightly past the average degree. The way traditional models
imprint assortativity on top of pre-defined topologies is via degree-preserving
link permutations, which however destroy the particular graph's hierarchical
traits of clustering. Here, we propose the first generative model which creates
heterogeneous networks with scale-free-like properties and tunable realistic
assortativity. In our approach, two distinct populations of nodes are added to
an initial network seed: one (the followers) that abides by usual preferential
rules, and one (the potential leaders) connecting via anti-preferential
attachments, i.e. selecting lower degree nodes for their initial links. The
latter nodes come to develop a higher average degree, and convert eventually
into the final hubs. Examining the evolution of links in Facebook, we present
empirical validation for the connection between the initial anti-preferential
attachment and long term high degree. Thus, our work sheds new light on the
structure and evolution of social networks
Detecting local synchronization in coupled chaotic systems
We introduce a technique to detect and quantify local functional dependencies
between coupled chaotic systems. The method estimates the fraction of locally
syncronized configurations, in a pair of signals with an arbitrary state of
global syncronization. Application to a pair of interacting Rossler oscillators
shows that our method is capable to quantify the number of dynamical
configurations where a local prediction task is possible, also in absence of
global synchronization features
Explosive synchronization in weighted complex networks
The emergence of dynamical abrupt transitions in the macroscopic state of a
system is currently a subject of the utmost interest. Given a set of phase
oscillators networking with a generic wiring of connections and displaying a
generic frequency distribution, we show how combining dynamical local
information on frequency mismatches and global information on the graph
topology suggests a judicious and yet practical weighting procedure which is
able to induce and enhance explosive, irreversible, transitions to
synchronization. We report extensive numerical and analytical evidence of the
validity and scalability of such a procedure for different initial frequency
distributions, for both homogeneous and heterogeneous networks, as well as for
both linear and non linear weighting functions. We furthermore report on the
possibility of parametrically controlling the width and extent of the
hysteretic region of coexistence of the unsynchronized and synchronized states
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