7,422 research outputs found
Synchronization of networks with prescribed degree distributions
We show that the degree distributions of graphs do not suffice to
characterize the synchronization of systems evolving on them. We prove that,
for any given degree sequence satisfying certain conditions, there exists a
connected graph having that degree sequence for which the first nontrivial
eigenvalue of the graph Laplacian is arbitrarily close to zero. Consequently,
complex dynamical systems defined on such graphs have poor synchronization
properties. The result holds under quite mild assumptions, and shows that there
exists classes of random, scale-free, regular, small-world, and other common
network architectures which impede synchronization. The proof is based on a
construction that also serves as an algorithm for building non-synchronizing
networks having a prescribed degree distribution.Comment: v2: A new theorem and a numerical example added. To appear in IEEE
Trans. Circuits and Systems I: Fundamental Theory and Application
Optimal global synchronization of partially forced Kuramoto oscillators
We consider the problem of global synchronization in a large random network
of Kuramoto oscillators where some of them are subject to an external
periodically driven force. We explore a recently proposed dimensional reduction
approach and introduce an effective two-dimensional description for the
problem. From the dimensionally reduced model, we obtain analytical predictions
for some critical parameters necessary for the onset of a globally synchronized
state in the system. Moreover, the low dimensional model also allows us to
introduce an optimization scheme for the problem. Our main conclusion, which
has been corroborated by exhaustive numerical simulations, is that for a given
large random network of Kuramoto oscillators, with random natural frequencies
, such that a fraction of them is subject to an external periodic
force with frequency , the best global synchronization properties
correspond to the case where the fraction of the forced oscillators is chosen
to be those ones such that is maximal. Our results might
shed some light on the structure and evolution of natural systems for which the
presence or the absence of global synchronization are desired properties. Some
properties of the optimal forced networks and its relation to recent results in
the literature are also discussed.Comment: 8 pages, 3 figures. Final version accepted for publication in Chaos.
After it is published, it will be found at
https://publishing.aip.org/resources/librarians/products/journals
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
Modeling self-sustained activity cascades in socio-technical networks
The ability to understand and eventually predict the emergence of information
and activation cascades in social networks is core to complex socio-technical
systems research. However, the complexity of social interactions makes this a
challenging enterprise. Previous works on cascade models assume that the
emergence of this collective phenomenon is related to the activity observed in
the local neighborhood of individuals, but do not consider what determines the
willingness to spread information in a time-varying process. Here we present a
mechanistic model that accounts for the temporal evolution of the individual
state in a simplified setup. We model the activity of the individuals as a
complex network of interacting integrate-and-fire oscillators. The model
reproduces the statistical characteristics of the cascades in real systems, and
provides a framework to study time-evolution of cascades in a state-dependent
activity scenario.Comment: 5 pages, 3 figure
Network synchronization: Spectral versus statistical properties
We consider synchronization of weighted networks, possibly with asymmetrical
connections. We show that the synchronizability of the networks cannot be
directly inferred from their statistical properties. Small local changes in the
network structure can sensitively affect the eigenvalues relevant for
synchronization, while the gross statistical network properties remain
essentially unchanged. Consequently, commonly used statistical properties,
including the degree distribution, degree homogeneity, average degree, average
distance, degree correlation, and clustering coefficient, can fail to
characterize the synchronizability of networks
Discovering universal statistical laws of complex networks
Different network models have been suggested for the topology underlying
complex interactions in natural systems. These models are aimed at replicating
specific statistical features encountered in real-world networks. However, it
is rarely considered to which degree the results obtained for one particular
network class can be extrapolated to real-world networks. We address this issue
by comparing different classical and more recently developed network models
with respect to their generalisation power, which we identify with large
structural variability and absence of constraints imposed by the construction
scheme. After having identified the most variable networks, we address the
issue of which constraints are common to all network classes and are thus
suitable candidates for being generic statistical laws of complex networks. In
fact, we find that generic, not model-related dependencies between different
network characteristics do exist. This allows, for instance, to infer global
features from local ones using regression models trained on networks with high
generalisation power. Our results confirm and extend previous findings
regarding the synchronisation properties of neural networks. Our method seems
especially relevant for large networks, which are difficult to map completely,
like the neural networks in the brain. The structure of such large networks
cannot be fully sampled with the present technology. Our approach provides a
method to estimate global properties of under-sampled networks with good
approximation. Finally, we demonstrate on three different data sets (C.
elegans' neuronal network, R. prowazekii's metabolic network, and a network of
synonyms extracted from Roget's Thesaurus) that real-world networks have
statistical relations compatible with those obtained using regression models
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