1,008 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
Divergent Time Scale in Axelrod Model Dynamics
We study the evolution of the Axelrod model for cultural diversity. We
consider a simple version of the model in which each individual is
characterized by two features, each of which can assume q possibilities. Within
a mean-field description, we find a transition at a critical value q_c between
an active state of diversity and a frozen state. For q just below q_c, the
density of active links between interaction partners is non-monotonic in time
and the asymptotic approach to the steady state is controlled by a time scale
that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma
Time scale competition leading to fragmentation and recombination transitions in the coevolution of network and states
We study the co-evolution of network structure and node states in a model of
multiple state interacting agents. The system displays two transitions, network
recombination and fragmentation, governed by time scales that emerge from the
dynamics. The recombination transition separates a frozen configuration,
composed by disconnected network components whose agents share the same state,
from an active configuration, with a fraction of links that are continuously
being rewired. The nature of this transition is explained analytically as the
maximum of a characteristic time. The fragmentation transition, that appears
between two absorbing frozen phases, is an anomalous order-disorder transition,
governed by a crossover between the time scales that control the structure and
state dynamics.Comment: 5 pages, 5 figures, figures 2 and 4 changed, tile changed, to be
published in PR
Information feedback and mass media effects in cultural dynamics
We study the effects of different forms of information feedback associated
with mass media on an agent-agent based model of the dynamics of cultural
dissemination. In addition to some processes previously considered, we also
examine a model of local mass media influence in cultural dynamics. Two
mechanisms of information feedback are investigated: (i) direct mass media
influence, where local or global mass media act as an additional element in the
network of interactions of each agent, and (ii) indirect mass media influence,
where global media acts as a filter of the influence of the existing network of
interactions of each agent. Our results generalize previous findings showing
that cultural diversity builds-up by increasing the strength of the mass media
influence. We find that this occurs independently of the mechanisms of action
(direct or indirect) of the mass media message. However, through an analysis of
the full range of parameters measuring cultural diversity, we establish that
the enhancement of cultural diversity produced by interaction with mass media
only occurs for strong enough mass media messages. In comparison with previous
studies a main different result is that weak mass media messages, in
combination with agent-agent interaction, are efficient in producing cultural
homogeneity. Moreover, the homogenizing effect of weak mass media messages are
more efficient for direct local mass media messages than for global mass media
messages or indirect global mass media influences.Comment: 20n pages, 10 figure
Resonance induced by repulsive interactions in a model of globally-coupled bistable systems
We show the existence of a competition-induced resonance effect for a generic
globally coupled bistable system. In particular, we demonstrate that the
response of the macroscopic variable to an external signal is optimal for a
particular proportion of repulsive links. Furthermore, we show that a resonance
also occurs for other system parameters, like the coupling strength and the
number of elements. We relate this resonance to the appearance of a multistable
region, and we predict the location of the resonance peaks, by a simple
spectral analysis of the Laplacian matrix
Nonlinear oscillator with parametric colored noise: some analytical results
The asymptotic behavior of a nonlinear oscillator subject to a multiplicative
Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in
terms of energy-angle coordinates, it is observed that the angle is a fast
variable as compared to the energy. Thus, an effective stochastic dynamics for
the energy can be derived if the angular variable is averaged out. However, the
standard elimination procedure, performed earlier for a Gaussian white noise,
fails when the noise is colored because of correlations between the noise and
the fast angular variable. We develop here a specific averaging scheme that
retains these correlations. This allows us to calculate the probability
distribution function (P.D.F.) of the system and to derive the behavior of
physical observables in the long time limit
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
Importance of single nodes in dynamics on networks
Identifying key players in collective dynamics remains a challenge in several research
fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The
difficulty lies at several levels: how to single out the role of individual elements in such intermingled
systems, or which is the best way to quantify their importance. Centrality measures describe a node's
importance by its position in a network. The key issue obviated is that the contribution of a node to
the collective behavior is not uniquely determined by the structure of the system but it is a result of the
interplay between dynamics and network structure
Importance of single nodes in dynamics on networks
Identifying key players in collective dynamics remains a challenge in several research
fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The
difficulty lies at several levels: how to single out the role of individual elements in such intermingled
systems, or which is the best way to quantify their importance. Centrality measures describe a node's
importance by its position in a network. The key issue obviated is that the contribution of a node to
the collective behavior is not uniquely determined by the structure of the system but it is a result of the
interplay between dynamics and network structure
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