232 research outputs found
Coupled dynamics of node and link states in complex networks: A model for language competition
Inspired by language competition processes, we present a model of coupled
evolution of node and link states. In particular, we focus on the interplay
between the use of a language and the preference or attitude of the speakers
towards it, which we model, respectively, as a property of the interactions
between speakers (a link state) and as a property of the speakers themselves (a
node state). Furthermore, we restrict our attention to the case of two socially
equivalent languages and to socially inspired network topologies based on a
mechanism of triadic closure. As opposed to most of the previous literature,
where language extinction is an inevitable outcome of the dynamics, we find a
broad range of possible asymptotic configurations, which we classify as: frozen
extinction states, frozen coexistence states, and dynamically trapped
coexistence states. Moreover, metastable coexistence states with very long
survival times and displaying a non-trivial dynamics are found to be abundant.
Interestingly, a system size scaling analysis shows, on the one hand, that the
probability of language extinction vanishes exponentially for increasing system
sizes and, on the other hand, that the time scale of survival of the
non-trivial dynamical metastable states increases linearly with the size of the
system. Thus, non-trivial dynamical coexistence is the only possible outcome
for large enough systems. Finally, we show how this coexistence is
characterized by one of the languages becoming clearly predominant while the
other one becomes increasingly confined to "ghetto-like" structures: small
groups of bilingual speakers arranged in triangles, with a strong preference
for the minority language, and using it for their intra-group interactions
while they switch to the predominant language for communications with the rest
of the population.Comment: 21 pages, 15 figure
The noisy voter model on complex networks
We propose a new analytical method to study stochastic, binary-state models
on complex networks. Moving beyond the usual mean-field theories, this
alternative approach is based on the introduction of an annealed approximation
for uncorrelated networks, allowing to deal with the network structure as
parametric heterogeneity. As an illustration, we study the noisy voter model, a
modification of the original voter model including random changes of state. The
proposed method is able to unfold the dependence of the model not only on the
mean degree (the mean-field prediction) but also on more complex averages over
the degree distribution. In particular, we find that the degree heterogeneity
---variance of the underlying degree distribution--- has a strong influence on
the location of the critical point of a noise-induced, finite-size transition
occurring in the model, on the local ordering of the system, and on the
functional form of its temporal correlations. Finally, we show how this latter
point opens the possibility of inferring the degree heterogeneity of the
underlying network by observing only the aggregate behavior of the system as a
whole, an issue of interest for systems where only macroscopic, population
level variables can be measured.Comment: 28 pages, 9 figure
Markets, herding and response to external information
We focus on the influence of external sources of information upon financial
markets. In particular, we develop a stochastic agent-based market model
characterized by a certain herding behavior as well as allowing traders to be
influenced by an external dynamic signal of information. This signal can be
interpreted as a time-varying advertising, public perception or rumor, in favor
or against one of two possible trading behaviors, thus breaking the symmetry of
the system and acting as a continuously varying exogenous shock. As an
illustration, we use a well-known German Indicator of Economic Sentiment as
information input and compare our results with Germany's leading stock market
index, the DAX, in order to calibrate some of the model parameters. We study
the conditions for the ensemble of agents to more accurately follow the
information input signal. The response of the system to the external
information is maximal for an intermediate range of values of a market
parameter, suggesting the existence of three different market regimes:
amplification, precise assimilation and undervaluation of incoming information.Comment: 30 pages, 8 figures. Thoroughly revised and updated version of
arXiv:1302.647
Monte Carlo method for the numerical simulation of Tsallis statistics
We present a new method devised to overcome the intrinsic difficulties associated to the numerical simulations of the Tsallis statistics. We use a standard Metropolis Monte Carlo algorithm at a fictitious temperature T′, combined with a numerical integration method for the calculation of the entropy in order to evaluate the actual temperature T. We illustrate the method by applying it to the 2d-Ising model using a standard reweighting technique.We acknowledge financial support from DGES, grants PB94-1167 and PB97- 0141-C02-01.Peer Reviewe
Fragmentation transition in a coevolving network with link-state dynamics
We study a network model that couples the dynamics of link states with the
evolution of the network topology. The state of each link, either A or B, is
updated according to the majority rule or zero-temperature Glauber dynamics, in
which links adopt the state of the majority of their neighboring links in the
network. Additionally, a link that is in a local minority is rewired to a
randomly chosen node. While large systems evolving under the majority rule
alone always fall into disordered topological traps composed by frustrated
links, any amount of rewiring is able to drive the network to complete order,
by relinking frustrated links and so releasing the system from traps. However,
depending on the relative rate of the majority rule and the rewiring processes,
the system evolves towards different ordered absorbing configurations: either a
one-component network with all links in the same state or a network fragmented
in two components with opposite states. For low rewiring rates and finite size
networks there is a domain of bistability between fragmented and non-fragmented
final states. Finite size scaling indicates that fragmentation is the only
possible scenario for large systems and any nonzero rate of rewiring.Comment: 10 pages, 13 figure
Binary and Multivariate Stochastic Models of Consensus Formation
A current paradigm in computer simulation studies of social sciences problems
by physicists is the emergence of consensus. The question is to establish when
the dynamics of a set of interacting agents that can choose among several
options (political vote, opinion, cultural features, etc.) leads to a consensus
in one of these options, or when a state with several coexisting social options
prevail. We consider here stochastic dynamic models naturally studied by
computer simulations. We will first review some basic results for the voter
model. This is a binary option stochastic model, and probably the simplest
model of collective behavior. Next we consider a model proposed by Axelrod for
the dissemination of culture. This model can be considered as a multivariable
elaboration of the voter model dynamics.Comment: (16 pages, 8 figures; for simililar work visit
http://www.imedea.uib.es/physdept
Order parameter expansion study of synchronous firing induced by quenched noise in the active rotator model
We use a recently developed order parameter expansion method to study the
transition to synchronous firing occuring in a system of coupled active
rotators under the exclusive presence of quenched noise. The method predicts
correctly the existence of a transition from a rest state to a regime of
synchronous firing and another transition out of it as the intensity of the
quenched noise increases and leads to analytical expressions for the critical
noise intensities in the large coupling regime. It also predicts the order of
the transitions for different probability distribution functions of the
quenched variables. We use numerical simulations and finite size scaling theory
to estimate the critical exponents of the transitions and found values which
are consistent with those reported in other scalar systems in the exclusive
presence of additive static disorder
Diversity and noise effects in a model of homeostatic regulation of the sleep-wake cycle
Recent advances in sleep neurobiology have allowed development of
physiologically based mathematical models of sleep regulation that account for
the neuronal dynamics responsible for the regulation of sleep-wake cycles and
allow detailed examination of the underlying mechanisms. Neuronal systems in
general, and those involved in sleep regulation in particular, are noisy and
heterogeneous by their nature. It has been shown in various systems that
certain levels of noise and diversity can significantly improve signal
encoding. However, these phenomena, especially the effects of diversity, are
rarely considered in the models of sleep regulation. The present paper is
focused on a neuron-based physiologically motivated model of sleep-wake cycles
that proposes a novel mechanism of the homeostatic regulation of sleep based on
the dynamics of a wake-promoting neuropeptide orexin. Here this model is
generalized by the introduction of intrinsic diversity and noise in the
orexin-producing neurons in order to study the effect of their presence on the
sleep-wake cycle. A quantitative measure of the quality of a sleep-wake cycle
is introduced and used to systematically study the generalized model for
different levels of noise and diversity. The model is shown to exhibit a clear
diversity-induced resonance: that is, the best wake-sleep cycle turns out to
correspond to an intermediate level of diversity at the synapses of the
orexin-producing neurons. On the other hand only a mild evidence of stochastic
resonance is found when the level of noise is varied. These results show that
disorder, especially in the form of quenched diversity, can be a key-element
for an efficient or optimal functioning of the homeostatic regulation of the
sleep-wake cycle. Furthermore, this study provides an example of constructive
role of diversity in a neuronal system that can be extended beyond the system
studied here.Comment: 18 pages, 12 figures, 1 tabl
Dynamical mechanism of anticipating synchronization in excitable systems
We analyze the phenomenon of anticipating synchronization of two excitable
systems with unidirectional delayed coupling which are subject to the same
external forcing. We demonstrate for different paradigms of excitable system
that, due to the coupling, the excitability threshold for the slave system is
always lower than that for the master. As a consequence the two systems respond
to a common external forcing with different response times. This allows to
explain in a simple way the mechanism behind the phenomenon of anticipating
synchronization.Comment: 4 pages including 7 figures. Submitted for publicatio
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