105 research outputs found
Dynamic Renormalization Group Approach to Self-Organized Critical Phenomena
Two different models exhibiting self-organized criticality are analyzed by
means of the dynamic renormalization group. Although the two models differ by
their behavior under a parity transformation of the order parameter, it is
shown that they both belong to the same universality class, in agreement with
computer simulations. The asymptotic values of the critical exponents are
estimated up to one loop order from a systematic expansion of a nonlinear
equation in the number of coupling constants.Comment: 8 pages, RevTeX 3.0, 1 PostScript figure available upon reques
Synchronization in a ring of pulsating oscillators with bidirectional couplings
We study the dynamical behavior of an ensemble of oscillators interacting
through short range bidirectional pulses. The geometry is 1D with periodic
boundary conditions. Our interest is twofold. To explore the conditions
required to reach fully synchronization and to invewstigate the time needed to
get such state. We present both theoretical and numerical results.Comment: Revtex, 4 pages, 2 figures. To appear in Int. J. Bifurc. and Chao
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
On Self-Organized Criticality and Synchronization in Lattice Models of Coupled Dynamical Systems
Lattice models of coupled dynamical systems lead to a variety of complex
behaviors. Between the individual motion of independent units and the
collective behavior of members of a population evolving synchronously, there
exist more complicated attractors. In some cases, these states are identified
with self-organized critical phenomena. In other situations, with
clusterization or phase-locking. The conditions leading to such different
behaviors in models of integrate-and-fire oscillators and stick-slip processes
are reviewed.Comment: 41 pages. Plain LaTeX. Style included in main file. To appear as an
invited review in Int. J. Modern Physics B. Needs eps
Pattern selection in a lattice of pulse-coupled oscillators
We study spatio-temporal pattern formation in a ring of N oscillators with
inhibitory unidirectional pulselike interactions. The attractors of the
dynamics are limit cycles where each oscillator fires once and only once. Since
some of these limit cycles lead to the same pattern, we introduce the concept
of pattern degeneracy to take it into account. Moreover, we give a qualitative
estimation of the volume of the basin of attraction of each pattern by means of
some probabilistic arguments and pattern degeneracy, and show how are they
modified as we change the value of the coupling strength. In the limit of small
coupling, our estimative formula gives a perfect agreement with numerical
simulations.Comment: 7 pages, 8 figures. To be published in Physical Review
The dynamics of norm change in the cultural evolution of language
What happens when a new social convention replaces an old one? While the possible forces favoring norm change - such as institutions or committed activists - have been identified since a long time, little is known about how a population adopts a new convention, due to the diffculties of finding representative data. Here we address this issue by looking at changes occurred to 2,541 orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years 1800 and 2008. We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority or a spontaneous process of unregulated evolution. We propose a simple evolutionary model able to capture all the observed behaviors and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior
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?
Dynamical and spectral properties of complex networks
Dynamical properties of complex networks are related to the spectral
properties of the Laplacian matrix that describes the pattern of connectivity
of the network. In particular we compute the synchronization time for different
types of networks and different dynamics. We show that the main dependence of
the synchronization time is on the smallest nonzero eigenvalue of the Laplacian
matrix, in contrast to other proposals in terms of the spectrum of the
adjacency matrix. Then, this topological property becomes the most relevant for
the dynamics.Comment: 14 pages, 5 figures, to be published in New Journal of Physic
Replicator dynamics with diffusion on multiplex networks
In this study we present an extension of the dynamics of diffusion in multiplex graphs, which makes the equations compatible with the replicator equation with mutations. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for nonlinear terms when working with fractions of individuals. We also derive the transition probabilities that give rise to such macroscopic behavior, completing the bottom-up description. Finally, it is shown that the usual assumption of constant population sizes induces a hidden selective pressure due to the diffusive dynamics, which favors the increase of fast diffusing strategies
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
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