88 research outputs found
Extracting topological features from dynamical measures in networks of Kuramoto oscillators
The Kuramoto model for an ensemble of coupled oscillators provides a
paradigmatic example of non-equilibrium transitions between an incoherent and a
synchronized state. Here we analyze populations of almost identical oscillators
in arbitrary interaction networks. Our aim is to extract topological features
of the connectivity pattern from purely dynamical measures, based on the fact
that in a heterogeneous network the global dynamics is not only affected by the
distribution of the natural frequencies, but also by the location of the
different values. In order to perform a quantitative study we focused on a very
simple frequency distribution considering that all the frequencies are equal
but one, that of the pacemaker node. We then analyze the dynamical behavior of
the system at the transition point and slightly above it, as well as very far
from the critical point, when it is in a highly incoherent state. The gathered
topological information ranges from local features, such as the single node
connectivity, to the hierarchical structure of functional clusters, and even to
the entire adjacency matrix.Comment: 11 pages, 10 figure
Synchronization in Random Geometric Graphs
In this paper we study the synchronization properties of random geometric
graphs. We show that the onset of synchronization takes place roughly at the
same value of the order parameter that a random graph with the same size and
average connectivity. However, the dependence of the order parameter with the
coupling strength indicates that the fully synchronized state is more easily
attained in random graphs. We next focus on the complete synchronized state and
show that this state is less stable for random geometric graphs than for other
kinds of complex networks. Finally, a rewiring mechanism is proposed as a way
to improve the stability of the fully synchronized state as well as to lower
the value of the coupling strength at which it is achieved. Our work has
important implications for the synchronization of wireless networks, and should
provide valuable insights for the development and deployment of more efficient
and robust distributed synchronization protocols for these systems.Comment: 5 pages, 4 figure
Symmetries and Fixed Point Stability of Stochastic Differential Equations Modeling Self-Organized Criticality
A stochastic nonlinear partial differential equation is built for two
different models exhibiting self-organized criticality, the Bak, Tang, and
Wiesenfeld (BTW) sandpile model and the Zhang's model. The dynamic
renormalization group (DRG) enables to compute the critical exponents. However,
the nontrivial stable fixed point of the DRG transformation is unreachable for
the original parameters of the models. We introduce an alternative
regularization of the step function involved in the threshold condition, which
breaks the symmetry of the BTW model. Although the symmetry properties of the
two models are different, it is shown that they both belong to the same
universality class. In this case the DRG procedure leads to a symmetric
behavior for both models, restoring the broken symmetry, and makes accessible
the nontrivial fixed point. This technique could also be applied to other
problems with threshold dynamics.Comment: 19 pages, RevTex, includes 6 PostScript figures, Phys. Rev. E (March
97?
Synchronization reveals topological scales in complex networks
We study the relationship between topological scales and dynamic time scales
in complex networks. The analysis is based on the full dynamics towards
synchronization of a system of coupled oscillators. In the synchronization
process, modular structures corresponding to well defined communities of nodes
emerge in different time scales, ordered in a hierarchical way. The analysis
also provides a useful connection between synchronization dynamics, complex
networks topology and spectral graph analysis.Comment: 4 pages, 3 figure
Modelling diffusion of innovations in a social network
A new simple model of diffusion of innovations in a social network with
upgrading costs is introduced. Agents are characterized by a single real
variable, their technological level. According to local information agents
decide whether to upgrade their level or not balancing their possible benefit
with the upgrading cost. A critical point where technological avalanches
display a power-law behavior is also found. This critical point is
characterized by a macroscopic observable that turns out to optimize
technological growth in the stationary state. Analytical results supporting our
findings are found for the globally coupled case.Comment: 4 pages, 5 figures. Final version accepted in PR
Communication in networks with hierarchical branching
We present a simple model of communication in networks with hierarchical
branching. We analyze the behavior of the model from the viewpoint of critical
systems under different situations. For certain values of the parameters, a
continuous phase transition between a sparse and a congested regime is observed
and accurately described by an order parameter and the power spectra. At the
critical point the behavior of the model is totally independent of the number
of hierarchical levels. Also scaling properties are observed when the size of
the system varies. The presence of noise in the communication is shown to break
the transition. Despite the simplicity of the model, the analytical results are
a useful guide to forecast the main features of real networks.Comment: 4 pages, 3 figures. Final version accepted in PR
Optimal network topologies for local search with congestion
The problem of searchability in decentralized complex networks is of great
importance in computer science, economy and sociology. We present a formalism
that is able to cope simultaneously with the problem of search and the
congestion effects that arise when parallel searches are performed, and obtain
expressions for the average search cost--written in terms of the search
algorithm and the topological properties of the network--both in presence and
abscence of congestion. This formalism is used to obtain optimal network
structures for a system using a local search algorithm. It is found that only
two classes of networks can be optimal: star-like configurations, when the
number of parallel searches is small, and homogeneous-isotropic configurations,
when the number of parallel searches is large.Comment: 4 pages. Final version accepted in PR
Correlations in Bipartite Collaboration Networks
Collaboration networks are studied as an example of growing bipartite
networks. These have been previously observed to have structure such as
positive correlations between nearest-neighbour degrees. However, a detailed
understanding of the origin of this phenomenon and the growth dynamics is
lacking. Both of these are analyzed empirically and simulated using various
models. A new one is presented, incorporating empirically necessary ingredients
such as bipartiteness and sublinear preferential attachment. This, and a
recently proposed model of team assembly both agree roughly with some empirical
observations and fail in several others.Comment: 13 pages, 17 figures, 2 table, submitted to JSTAT; manuscript
reorganized, figures and a table adde
Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
Universality in isotropic, abelian and non-abelian, sandpile models is
examined using extensive numerical simulations. To characterize the critical
behavior we employ an extended set of critical exponents, geometric features of
the avalanches, as well as scaling functions describing the time evolution of
average quantities such as the area and size during the avalanche. Comparing
between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K.
Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models
introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C.
Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each
one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file
Disorder-induced critical behavior in driven diffusive systems
Using dynamic renormalization group we study the transport in driven
diffusive systems in the presence of quenched random drift velocity with
long-range correlations along the transport direction. In dimensions
we find fixed points representing novel universality classes of
disorder-dominated self-organized criticality, and a continuous phase
transition at a critical variance of disorder. Numerical values of the scaling
exponents characterizing the distributions of relaxation clusters are in good
agreement with the exponents measured in natural river networks
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