48 research outputs found
Dynamical Organization of Cooperation in Complex Topologies
In this Letter, we study how cooperation is organized in complex topologies
by analyzing the evolutionary (replicator) dynamics of the Prisoner's Dilemma,
a two-players game with two available strategies, defection and cooperation,
whose payoff matrix favors defection. We show that, asymptotically, the
population is partitioned into three subsets: individuals that always cooperate
({\em pure cooperators}), always defect ({\em pure defectors}) and those that
intermittently change their strategy. In fact the size of the latter set is the
biggest for a wide range of the "stimulus to defect" parameter. While in
homogeneous random graphs pure cooperators are grouped into several clusters,
in heterogeneous scale-free (SF) networks they always form a single cluster
containing the most connected individuals (hubs). Our results give further
insights into why cooperation in SF networks is favored.Comment: 4 pages and 4 figures. Final version as published in Physical Review
Letter
Residential segregation and cultural dissemination: An Axelrod-Schelling model
In the Axelrod's model of cultural dissemination, we consider mobility of
cultural agents through the introduction of a density of empty sites and the
possibility that agents in a dissimilar neighborhood can move to them if their
mean cultural similarity with the neighborhood is below some threshold. While
for low values of the density of empty sites the mobility enhances the
convergence to a global culture, for high enough values of it the dynamics can
lead to the coexistence of disconnected domains of different cultures. In this
regime, the increase of initial cultural diversity paradoxically increases the
convergence to a dominant culture. Further increase of diversity leads to
fragmentation of the dominant culture into domains, forever changing in shape
and number, as an effect of the never ending eroding activity of cultural
minorities
Internal mode mechanism for collective energy transport in extended systems
We study directed energy transport in homogeneous nonlinear extended systems
in the presence of homogeneous ac forces and dissipation. We show that the
mechanism responsible for unidirectional motion of topological excitations is
the coupling of their internal and translation degrees of freedom. Our results
lead to a selection rule for the existence of such motion based on resonances
that explains earlier symmetry analysis of this phenomenon. The direction of
motion is found to depend both on the initial and the relative phases of the
two harmonic drivings, even in the presence of noise.Comment: Final version, to appear in Physical Review Letter
Scale-Free topologies and Activatory-Inhibitory interactions
A simple model of activatory-inhibitory interactions controlling the activity
of agents (substrates) through a "saturated response" dynamical rule in a
scale-free network is thoroughly studied. After discussing the most remarkable
dynamical features of the model, namely fragmentation and multistability, we
present a characterization of the temporal (periodic and chaotic) fluctuations
of the quasi-stasis asymptotic states of network activity. The double (both
structural and dynamical) source of entangled complexity of the system temporal
fluctuations, as an important partial aspect of the Correlation
Structure-Function problem, is further discussed to the light of the numerical
results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major
revision and new results incorporated. To appear in Chaos (2006
Spreading of Persistent Infections in Heterogeneous Populations
Up to now, the effects of having heterogeneous networks of contacts have been
studied mostly for diseases which are not persistent in time, i.e., for
diseases where the infectious period can be considered very small compared to
the lifetime of an individual. Moreover, all these previous results have been
obtained for closed populations, where the number of individuals does not
change during the whole duration of the epidemics. Here, we go one step further
and analyze, both analytically and numerically, a radically different kind of
diseases: those that are persistent and can last for an individual's lifetime.
To be more specific, we particularize to the case of Tuberculosis' (TB)
infection dynamics, where the infection remains latent for a period of time
before showing up and spreading to other individuals. We introduce an
epidemiological model for TB-like persistent infections taking into account the
heterogeneity inherent to the population structure. This sort of dynamics
introduces new analytical and numerical challenges that we are able to sort
out. Our results show that also for persistent diseases the epidemic threshold
depends on the ratio of the first two moments of the degree distribution so
that it goes to zero in a class of scale-free networks when the system
approaches the thermodynamic limit.Comment: 12 pages and 2 figures. Revtex format. Submitted for publication
Social Network Reciprocity as a Phase Transition in Evolutionary Cooperation
In Evolutionary Dynamics the understanding of cooperative phenomena in
natural and social systems has been the subject of intense research during
decades. We focus attention here on the so-called "Lattice Reciprocity"
mechanisms that enhance evolutionary survival of the cooperative phenotype in
the Prisoner's Dilemma game when the population of darwinian replicators
interact through a fixed network of social contacts. Exact results on a "Dipole
Model" are presented, along with a mean-field analysis as well as results from
extensive numerical Monte Carlo simulations. The theoretical framework used is
that of standard Statistical Mechanics of macroscopic systems, but with no
energy considerations. We illustrate the power of this perspective on social
modeling, by consistently interpreting the onset of lattice reciprocity as a
thermodynamical phase transition that, moreover, cannot be captured by a purely
mean-field approach.Comment: 10 pages. APS styl
Contests in two fronts
Within the framework of Game Theory, contests study decision-making in those
situations or conflicts when rewards depend on the relative rank between
contenders rather than their absolute performance. By relying on the formalism
of Tullock success functions, we propose a model where two contenders fight in
a conflict on two fronts with different technology levels associated: a front
with large resource demand and another with lower resource requirements. The
parameter of the success function in each front determines the resource demand
level. Furthermore, the redistribution or not of resources after a tie defines
two different games. We solve the model analytically through the best-response
map dynamics, finding a critical threshold for the ratio of the resources
between contenders that determines the Nash Equilibrium basin and,
consequently, the peace and fighting regimes. We also perform numerical
simulations that corroborate and extend these findings. We hope this study will
be of interest to areas as diverse as economic conflicts and geopolitics.Comment: 21 pages, 11 figure
Discrete breathers in dissipative lattices
We study the properties of discrete breathers, also known as intrinsic
localized modes, in the one-dimensional Frenkel-Kontorova lattice of
oscillators subject to damping and external force. The system is studied in the
whole range of values of the coupling parameter, from C=0 (uncoupled limit) up
to values close to the continuum limit (forced and damped sine-Gordon model).
As this parameter is varied, the existence of different bifurcations is
investigated numerically. Using Floquet spectral analysis, we give a complete
characterization of the most relevant bifurcations, and we find (spatial)
symmetry-breaking bifurcations which are linked to breather mobility, just as
it was found in Hamiltonian systems by other authors. In this way moving
breathers are shown to exist even at remarkably high levels of discreteness. We
study mobile breathers and characterize them in terms of the phonon radiation
they emit, which explains successfully the way in which they interact. For
instance, it is possible to form ``bound states'' of moving breathers, through
the interaction of their phonon tails. Over all, both stationary and moving
breathers are found to be generic localized states over large values of ,
and they are shown to be robust against low temperature fluctuations.Comment: To be published in Physical Review