11,711 research outputs found
Paths to Synchronization on Complex Networks
The understanding of emergent collective phenomena in natural and social
systems has driven the interest of scientists from different disciplines during
decades. Among these phenomena, the synchronization of a set of interacting
individuals or units has been intensively studied because of its ubiquity in
the natural world. In this paper, we show how for fixed coupling strengths
local patterns of synchronization emerge differently in homogeneous and
heterogeneous complex networks, driving the process towards a certain global
synchronization degree following different paths. The dependence of the
dynamics on the coupling strength and on the topology is unveiled. This study
provides a new perspective and tools to understand this emerging phenomena.Comment: Final version published in Physical Review Letter
Explosive Synchronization Transitions in Scale-free Networks
The emergence of explosive collective phenomena has recently attracted much
attention due to the discovery of an explosive percolation transition in
complex networks. In this Letter, we demonstrate how an explosive transition
shows up in the synchronization of complex heterogeneous networks by
incorporating a microscopic correlation between the structural and the
dynamical properties of the system. The characteristics of this explosive
transition are analytically studied in a star graph reproducing the results
obtained in synthetic scale-free networks. Our findings represent the first
abrupt synchronization transition in complex networks thus providing a deeper
understanding of the microscopic roots of explosive critical phenomena.Comment: 6 pages and 5 figures. To appear in Physical Review Letter
Explosive first-order transition to synchrony in networked chaotic oscillators
Critical phenomena in complex networks, and the emergence of dynamical abrupt
transitions in the macroscopic state of the system are currently a subject of
the outmost interest. We report evidence of an explosive phase synchronization
in networks of chaotic units. Namely, by means of both extensive simulations of
networks made up of chaotic units, and validation with an experiment of
electronic circuits in a star configuration, we demonstrate the existence of a
first order transition towards synchronization of the phases of the networked
units. Our findings constitute the first prove of this kind of synchronization
in practice, thus opening the path to its use in real-world applications.Comment: Phys. Rev. Lett. in pres
Synchronization of networks with variable local properties
We study the synchronization transition of Kuramoto oscillators in scale-free
networks that are characterized by tunable local properties. Specifically, we
perform a detailed finite size scaling analysis and inspect how the critical
properties of the dynamics change when the clustering coefficient and the
average shortest path length are varied. The results show that the onset of
synchronization does depend on these properties, though the dependence is
smooth. On the contrary, the appearance of complete synchronization is
radically affected by the structure of the networks. Our study highlights the
need of exploring the whole phase diagram and not only the stability of the
fully synchronized state, where most studies have been done up to now.Comment: 5 pages and 3 figures. APS style. Paper to be published in IJBC
(special issue on Complex Networks' Structure and Dynamics
Improved routing strategies for Internet traffic delivery
We analyze different strategies aimed at optimizing routing policies in the
Internet. We first show that for a simple deterministic algorithm the local
properties of the network deeply influence the time needed for packet delivery
between two arbitrarily chosen nodes. We next rely on a real Internet map at
the autonomous system level and introduce a score function that allows us to
examine different routing protocols and their efficiency in traffic handling
and packet delivery. Our results suggest that actual mechanisms are not the
most efficient and that they can be integrated in a more general, though not
too complex, scheme.Comment: Final versio
Synchronizability determined by coupling strengths and topology on Complex Networks
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.Comment: 11 pages, 10 figures and 1 table. APS forma
Diffusion dynamics on multiplex networks
We study the time scales associated to diffusion processes that take place on
multiplex networks, i.e. on a set of networks linked through interconnected
layers. To this end, we propose the construction of a supra-Laplacian matrix,
which consists of a dimensional lifting of the Laplacian matrix of each layer
of the multiplex network. We use perturbative analysis to reveal analytically
the structure of eigenvectors and eigenvalues of the complete network in terms
of the spectral properties of the individual layers. The spectrum of the
supra-Laplacian allows us to understand the physics of diffusion-like processes
on top of multiplex networks.Comment: 6 Pages including supplemental material. To appear in Physical Review
Letter
Exceptional orthogonal polynomials and the Darboux transformation
We adapt the notion of the Darboux transformation to the context of
polynomial Sturm-Liouville problems. As an application, we characterize the
recently described Laguerre polynomials in terms of an isospectral
Darboux transformation. We also show that the shape-invariance of these new
polynomial families is a direct consequence of the permutability property of
the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction
A conjecture on Exceptional Orthogonal Polynomials
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of
Sturm-Liouville problems and generalize in this sense the classical families of
Hermite, Laguerre and Jacobi. They also generalize the family of CPRS
orthogonal polynomials. We formulate the following conjecture: every
exceptional orthogonal polynomial system is related to a classical system by a
Darboux-Crum transformation. We give a proof of this conjecture for codimension
2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this
analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The
classification includes all cases known to date plus some new examples of
X2-Laguerre and X2-Jacobi polynomials
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