404 research outputs found
Synchronisation Induced by Repulsive Interactions in a System of van der Pol Oscillators
We consider a system of identical van der Pol oscillators, globally coupled
through their velocities, and study how the presence of competitive
interactions affects its synchronisation properties. We will address the
question from two points of view. Firstly, we will investigate the role of
competitive interactions on the synchronisation among identical oscillators.
Then, we will show that the presence of an intermediate fraction of repulsive
links results in the appearance of macroscopic oscillations at that signal's
rhythm, in regions where the individual oscillator is unable to synchronise
with a weak external signal
Divide and conquer: resonance induced by competitive interactions
We study an Ising model in a network with disorder induced by the presence of
both attractive and repulsive links. This system is subjected to a subthreshold
signal, and the goal is to see how the response is enhanced for a given
fraction of repulsive links. This can model a network of spin-like neurons with
excitatory and inhibitory couplings. By means of numerical simulations and
analytical calculations we find that there is an optimal probability, such that
the coherent response is maximal
Noisy continuous--opinion dynamics
We study the Deffuant et al. model for continuous--opinion dynamics under the
influence of noise. In the original version of this model, individuals meet in
random pairwise encounters after which they compromise or not depending of a
confidence parameter. Free will is introduced in the form of noisy
perturbations: individuals are given the opportunity to change their opinion,
with a given probability, to a randomly selected opinion inside the whole
opinion space. We derive the master equation of this process. One of the main
effects of noise is to induce an order-disorder transition. In the disordered
state the opinion distribution tends to be uniform, while for the ordered state
a set of well defined opinion groups are formed, although with some opinion
spread inside them. Using a linear stability analysis we can derive approximate
conditions for the transition between opinion groups and the disordered state.
The master equation analysis is compared with direct Monte-Carlo simulations.
We find that the master equation and the Monte-Carlo simulations do not always
agree due to finite-size induced fluctuations that we analyze in some detail
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
Two species coagulation approach to consensus by group level interactions
We explore the self-organization dynamics of a set of entities by considering
the interactions that affect the different subgroups conforming the whole. To
this end, we employ the widespread example of coagulation kinetics, and
characterize which interaction types lead to consensus formation and which do
not, as well as the corresponding different macroscopic patterns. The crucial
technical point is extending the usual one species coagulation dynamics to the
two species one. This is achieved by means of introducing explicitly solvable
kernels which have a clear physical meaning. The corresponding solutions are
calculated in the long time limit, in which consensus may or may not be
reached. The lack of consensus is characterized by means of scaling limits of
the solutions. The possible applications of our results to some topics in which
consensus reaching is fundamental, like collective animal motion and opinion
spreading dynamics, are also outlined
Phase Separation Driven by External Fluctuations
The influence of external fluctuations in phase separation processes is
analysed. These fluctuations arise from random variations of an external
control parameter. A linear stability analysis of the homogeneous state shows
that phase separation dynamics can be induced by external noise. The spatial
structure of the noise is found to have a relevant role in this phenomenon.
Numerical simulations confirm these results. A comparison with order-disorder
noise induced phase transitions is also made.Comment: 4 pages, 4 Postscript figures included in text. LaTeX (with Revtex
macros
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
Role of social environment and social clustering in spread of opinions in co-evolving networks
Taking a pragmatic approach to the processes involved in the phenomena of
collective opinion formation, we investigate two specific modifications to the
co-evolving network voter model of opinion formation, studied by Holme and
Newman [1]. First, we replace the rewiring probability parameter by a
distribution of probability of accepting or rejecting opinions between
individuals, accounting for the asymmetric influences in relationships among
individuals in a social group. Second, we modify the rewiring step by a
path-length-based preference for rewiring that reinforces local clustering. We
have investigated the influences of these modifications on the outcomes of the
simulations of this model. We found that varying the shape of the distribution
of probability of accepting or rejecting opinions can lead to the emergence of
two qualitatively distinct final states, one having several isolated connected
components each in internal consensus leading to the existence of diverse set
of opinions and the other having one single dominant connected component with
each node within it having the same opinion. Furthermore, and more importantly,
we found that the initial clustering in network can also induce similar
transitions. Our investigation also brings forward that these transitions are
governed by a weak and complex dependence on system size. We found that the
networks in the final states of the model have rich structural properties
including the small world property for some parameter regimes. [1] P. Holme and
M. Newman, Phys. Rev. E 74, 056108 (2006)
- …