11,694 research outputs found
A Generalized Sznajd Model
In the last decade the Sznajd Model has been successfully employed in
modeling some properties and scale features of both proportional and majority
elections. We propose a new version of the Sznajd model with a generalized
bounded confidence rule - a rule that limits the convincing capability of
agents and that is essential to allow coexistence of opinions in the stationary
state. With an appropriate choice of parameters it can be reduced to previous
models. We solved this new model both in a mean-field approach (for an
arbitrary number of opinions) and numerically in a Barabasi-Albert network (for
three and four opinions), studying the transient and the possible stationary
states. We built the phase portrait for the special cases of three and four
opinions, defining the attractors and their basins of attraction. Through this
analysis, we were able to understand and explain discrepancies between
mean-field and simulation results obtained in previous works for the usual
Sznajd Model with bounded confidence and three opinions. Both the dynamical
system approach and our generalized bounded confidence rule are quite general
and we think it can be useful to the understanding of other similar models.Comment: 19 pages with 8 figures. Submitted to Physical Review
Connections between the Sznajd Model with General Confidence Rules and graph theory
The Sznajd model is a sociophysics model, that is used to model opinion
propagation and consensus formation in societies. Its main feature is that its
rules favour bigger groups of agreeing people. In a previous work, we
generalized the bounded confidence rule in order to model biases and prejudices
in discrete opinion models. In that work, we applied this modification to the
Sznajd model and presented some preliminary results. The present work extends
what we did in that paper. We present results linking many of the properties of
the mean-field fixed points, with only a few qualitative aspects of the
confidence rule (the biases and prejudices modelled), finding an interesting
connection with graph theory problems. More precisely, we link the existence of
fixed points with the notion of strongly connected graphs and the stability of
fixed points with the problem of finding the maximal independent sets of a
graph. We present some graph theory concepts, together with examples, and
comparisons between the mean-field and simulations in Barab\'asi-Albert
networks, followed by the main mathematical ideas and appendices with the
rigorous proofs of our claims. We also show that there is no qualitative
difference in the mean-field results if we require that a group of size q>2,
instead of a pair, of agreeing agents be formed before they attempt to convince
other sites (for the mean-field, this would coincide with the q-voter model).Comment: 15 pages, 18 figures. To be submitted to Physical Revie
Two repelling random walks on
We consider two interacting random walks on such that the
transition probability of one walk in one direction decreases exponentially
with the number of transitions of the other walk in that direction. The joint
process may thus be seen as two random walks reinforced to repel each other.
The strength of the repulsion is further modulated in our model by a parameter
. When both processes are independent symmetric
random walks on , and hence recurrent. We show that both random
walks are further recurrent if . We also show that these
processes are transient and diverge in opposite directions if . The
case remains widely open. Our results are obtained by
considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument
for the convergence to equilibria of the vector field. Improved the proof for
the recurrence when beta belongs to (0,1); leading to the removal of a
previous conjectur
Optimal Trajectories for Near-Earth-Objects Using Solar Electric Propulsion (SEP) and Gravity Assisted Maneuver
The future interplanetary missions will probably use the conventional chemical rockets to leave the sphere of influence of the Earth, and solar electric propulsion (SEP) to accomplish the other maneuvers of the mission. In this work the optimization of interplanetary missions using solar electric propulsion and Gravity Assisted Maneuver to reduce the costs of the mission, is considered. The high specific impulse of electric propulsion makes a Gravity Assisted Maneuver 1 year after departure convenient. Missions for several Near Earth Asteroids will be considered. The analysis suggests criteria for the definition of initial solutions demanded for the process of optimization of trajectories. Trajectories for the asteroid 2002TC70 are analyzed. Direct trajectories, trajectories with 1 gravity assisted from the Earth and with 2 gravity assisted from the Earth and either Mars are present. An indirect optimization method will be used in the simulations
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