87 research outputs found
Update rules and interevent time distributions: Slow ordering vs. no ordering in the Voter Model
We introduce a general methodology of update rules accounting for arbitrary
interevent time distributions in simulations of interacting agents. In
particular we consider update rules that depend on the state of the agent, so
that the update becomes part of the dynamical model. As an illustration we
consider the voter model in fully-connected, random and scale free networks
with an update probability inversely proportional to the persistence, that is,
the time since the last event. We find that in the thermodynamic limit, at
variance with standard updates, the system orders slowly. The approach to the
absorbing state is characterized by a power law decay of the density of
interfaces, observing that the mean time to reach the absorbing state might be
not well defined.Comment: 5pages, 4 figure
Dynamics of link states in complex networks: The case of a majority rule
Motivated by the idea that some characteristics are specific to the relations
between individuals and not of the individuals themselves, we study a prototype
model for the dynamics of the states of the links in a fixed network of
interacting units. Each link in the network can be in one of two equivalent
states. A majority link-dynamics rule is implemented, so that in each dynamical
step the state of a randomly chosen link is updated to the state of the
majority of neighboring links. Nodes can be characterized by a link
heterogeneity index, giving a measure of the likelihood of a node to have a
link in one of the two states. We consider this link-dynamics model on fully
connected networks, square lattices and Erd \"os-Renyi random networks. In each
case we find and characterize a number of nontrivial asymptotic configurations,
as well as some of the mechanisms leading to them and the time evolution of the
link heterogeneity index distribution. For a fully connected network and random
networks there is a broad distribution of possible asymptotic configurations.
Most asymptotic configurations that result from link-dynamics have no
counterpart under traditional node dynamics in the same topologies.Comment: 9 pages, 13 figure
The Complex Ginzburg-Landau Equation in the Presence of Walls and Corners
We investigate the influence of walls and corners (with Dirichlet and Neumann
boundary conditions) in the evolution of twodimensional autooscillating fields
described by the complex Ginzburg-Landau equation. Analytical solutions are
found, and arguments provided, to show that Dirichlet walls introduce strong
selection mechanisms for the wave pattern. Corners between walls provide
additional synchronization mechanisms and associated selection criteria. The
numerical results fit well with the theoretical predictions in the parameter
range studied.Comment: 10 pages, 9 figures; for related work visit
http://www.nbi.dk/~martine
Conservation laws for the voter model in complex networks
We consider the voter model dynamics in random networks with an arbitrary
distribution of the degree of the nodes. We find that for the usual node-update
dynamics the average magnetization is not conserved, while an average
magnetization weighted by the degree of the node is conserved. However, for a
link-update dynamics the average magnetization is still conserved. For the
particular case of a Barabasi-Albert scale-free network the voter model
dynamics leads to a partially ordered metastable state with a finite size
survival time. This characteristic time scales linearly with system size only
when the updating rule respects the conservation law of the average
magnetization. This scaling identifies a universal or generic property of the
voter model dynamics associated with the conservation law of the magnetization.Comment: 5 pages, 4 figures; for related material please visit
http://www.imedea.uib.e
Shock structures in time averaged patterns for the Kuramoto-Sivashinsky equation
The Kuramoto-Sivashinsky equation with fixed boundary conditions is
numerically studied. Shocklike structures appear in the time-averaged patterns
for some parameter range of the boundary values. Effective diffusion constant
is estimated from the relation of the width and the height of the shock
structures.Comment: 6 pages, 7 figure
Heterogeneity shapes groups growth in social online communities
Many complex systems are characterized by broad distributions capturing, for
example, the size of firms, the population of cities or the degree distribution
of complex networks. Typically this feature is explained by means of a
preferential growth mechanism. Although heterogeneity is expected to play a
role in the evolution it is usually not considered in the modeling probably due
to a lack of empirical evidence on how it is distributed. We characterize the
intrinsic heterogeneity of groups in an online community and then show that
together with a simple linear growth and an inhomogeneous birth rate it
explains the broad distribution of group members.Comment: 5 pages, 3 figure panel
Quasiperiodic Patterns in Boundary-Modulated Excitable Waves
We investigate the impact of the domain shape on wave propagation in
excitable media. Channelled domains with sinusoidal boundaries are considered.
Trains of fronts generated periodically at an extreme of the channel are found
to adopt a quasiperiodic spatial configuration stroboscopically frozen in time.
The phenomenon is studied in a model for the photo-sensitive
Belousov-Zabotinsky reaction, but we give a theoretical derivation of the
spatial return maps prescribing the height and position of the successive
fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included
Anomalous lifetime distributions and topological traps in ordering dynamics
We address the role of community structure of an interaction network in
ordering dynamics, as well as associated forms of metastability. We consider
the voter and AB model dynamics in a network model which mimics social
interactions. The AB model includes an intermediate state between the two
excluding options of the voter model. For the voter model we find dynamical
metastable disordered states with a characteristic mean lifetime. However, for
the AB dynamics we find a power law distribution of the lifetime of metastable
states, so that the mean lifetime is not representative of the dynamics. These
trapped metastable states, which can order at all time scales, originate in the
mesoscopic network structure.Comment: 7 pages; 6 figure
Perturbation: the Catastrophe Causer in Scale-Free Networks
A new model about cascading occurrences caused by perturbation is established
to search after the mechanism because of which catastrophes in networks occur.
We investigate the avalanche dynamics of our model on 2-dimension Euclidean
lattices and scale-free networks and find out the avalanche dynamic behaviors
is very sensitive to the topological structure of networks. The experiments
show that the catastrophes occur much more frequently in scale-free networks
than in Euclidean lattices and the greatest catastrophe in scale-free networks
is much more serious than that in Euclidean lattices. Further more, we have
studied how to reduce the catastrophes' degree, and have schemed out an
effective strategy, called targeted safeguard-strategy for scale-free networks.Comment: 4 pages, 6 eps figure
Analytical Solution of the Voter Model on Disordered Networks
We present a mathematical description of the voter model dynamics on
heterogeneous networks. When the average degree of the graph is
the system reaches complete order exponentially fast. For , a finite
system falls, before it fully orders, in a quasistationary state in which the
average density of active links (links between opposite-state nodes) in
surviving runs is constant and equal to , while an
infinite large system stays ad infinitum in a partially ordered stationary
active state. The mean life time of the quasistationary state is proportional
to the mean time to reach the fully ordered state , which scales as , where is the number of nodes of the
network, and is the second moment of the degree distribution. We find
good agreement between these analytical results and numerical simulations on
random networks with various degree distributions.Comment: 20 pages, 8 figure
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