78 research outputs found
Diversity-induced resonance in a model for opinion formation
We study an opinion formation model that takes into account that individuals have diverse preferences when adopting an opinion regarding a particular issue. We show that the system exhibits "diversity-induced resonance” [C.J. Tessone et al. Phys. Rev. Lett. 97, 194101 (2006)], by which an external influence (for example advertising, or fashion trends) is better followed by populations having the right degree of diversity in their preferences, rather than others where the individuals are identical or have too different preferences. We support our findings by numerical simulations of the model in different network topologies and a mean-field type analytical theor
Global firing induced by network disorder in ensembles of active rotators
We study the influence of repulsive interactions on an ensemble of coupled
excitable rotators. We find that a moderate fraction of repulsive interactions
can trigger global firing of the ensemble. The regime of global firing,
however, is suppressed in sufficiently large systems if the network of
repulsive interactions is fully random, due to self-averaging in its degree
distribution. We thus introduce a model of partially random networks with a
broad degree distribution, where self-averaging due to size growth is absent.
In this case, the regime of global firing persists for large sizes. Our results
extend previous work on the constructive effects of diversity in the collective
dynamics of complex systems.Comment: 8 pages, 6 figure
Neighborhood models of minority opinion spreading
We study the effect of finite size population in Galam's model [Eur. Phys. J.
B 25 (2002) 403] of minority opinion spreading and introduce neighborhood
models that account for local spatial effects. For systems of different sizes
N, the time to reach consensus is shown to scale as ln N in the original
version, while the evolution is much slower in the new neighborhood models. The
threshold value of the initial concentration of minority supporters for the
defeat of the initial majority, which is independent of N in Galam's model,
goes to zero with growing system size in the neighborhood models. This is a
consequence of the existence of a critical size for the growth of a local
domain of minority supporters
A complementary view on the growth of directory trees
Trees are a special sub-class of networks with unique properties, such as the level distribution which has often been overlooked. We analyse a general tree growth model proposed by Klemm etal.[Phys. Rev. Lett. 95, 128701 (2005)] to explain the growth of user-generated directory structures in computers. The model has a single parameter q which interpolates between preferential attachment and random growth. Our analysis results in three contributions: first, we propose a more efficient estimation method for q based on the degree distribution, which is one specific representation of the model. Next, we introduce the concept of a level distribution and analytically solve the model for this representation. This allows for an alternative and independent measure of q. We argue that, to capture real growth processes, the q estimations from the degree and the level distributions should coincide. Thus, we finally apply both representations to validate the model with synthetically generated tree structures, as well as with collected data of user directories. In the case of real directory structures, we show that q measured from the level distribution are incompatible with q measured from the degree distribution. In contrast to this, we find perfect agreement in the case of simulated data. Thus, we conclude that the model is an incomplete description of the growth of real directory structures as it fails to reproduce the level distribution. This insight can be generalised to point out the importance of the level distribution for modeling tree growt
Global firing induced by network disorder in ensembles of activerotators
Abstract.: We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex system
Diversity-induced resonance
We present conclusive evidence showing that different sources of diversity,
such as those represented by quenched disorder or noise, can induce a resonant
collective behavior in an ensemble of coupled bistable or excitable systems.
Our analytical and numerical results show that when such systems are subjected
to an external subthreshold signal, their response is optimized for an
intermediate value of the diversity. These findings show that intrinsic
diversity might have a constructive role and suggest that natural systems might
profit from their diversity in order to optimize the response to an external
stimulus.Comment: 4 pages, 3 figure
Non-universal results induced by diversity distribution in coupled excitable systems
We consider a system of globally coupled active rotators near the excitable
regime. The system displays a transition to a state of collective firing
induced by disorder. We show that this transition is found generically for any
diversity distribution with well defined moments. Singularly, for the
Lorentzian distribution (widely used in Kuramoto-like systems) the transition
is not present. This warns about the use of Lorentzian distributions to
understand the generic properties of coupled oscillators
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Chaotic, staggered and polarized dynamics in opinion forming: the contrarian effect
We revisit the no tie breaking 2-state Galam contrarian model of opinion
dynamics for update groups of size 3. While the initial model assumes a
constant density of contrarians a for both opinions, it now depends for each
opinion on its global support. Proportionate contrarians are thus found to
indeed preserve the former case main results. However, restricting the
contrarian behavior to only the current collective majority, makes the dynamics
more complex with novel features. For a density a<a_c=1/9 of one-sided
contrarians, a chaotic basin is found in the fifty-fifty region separated from
two majority-minority point attractors, one on each side. For 1/9<a< 0.301 only
the chaotic basin survives. In the range a>0.301 the chaotic basin disappears
and the majority starts to alternate between the two opinions with a staggered
flow towards two point attractors. We then study the effect of both, decoupling
the local update time sequence from the contrarian behavior activation, and a
smoothing of the majority rule. A status quo driven bias for contrarian
activation is also considered. Introduction of unsettled agents driven in the
debate on a contrarian basis is shown to only shrink the chaotic basin. The
model may shed light to recent apparent contradictory elections with on the one
hand very tied results like in US in 2000 and in Germany in 2002 and 2005, and
on the other hand, a huge majority like in France in 2002.Comment: 17 pages, 10 figure
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