11,904 research outputs found
Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
Systems with long-range interactions often exhibit power-law distributions
and can by described by the non-extensive statistical mechanics framework
proposed by Tsallis. In this contribution we consider a simple model
reproducing continuous transition from the extensive to the non-extensive
statistics. The considered model is composed of agents interacting among
themselves on a certain network topology. To generate the underlying network we
propose a new network formation algorithm, in which the mean degree scales
sub-linearly with a number of nodes in the network (the scaling depends on a
single parameter). By changing this parameter we are able to continuously
transition from short-range to long-range interactions in the agent-based
model.Comment: 12 pages, 6 figure
The Bounded Confidence Model Of Opinion Dynamics
The bounded confidence model of opinion dynamics, introduced by Deffuant et
al, is a stochastic model for the evolution of continuous-valued opinions
within a finite group of peers. We prove that, as time goes to infinity, the
opinions evolve globally into a random set of clusters too far apart to
interact, and thereafter all opinions in every cluster converge to their
barycenter. We then prove a mean-field limit result, propagation of chaos: as
the number of peers goes to infinity in adequately started systems and time is
rescaled accordingly, the opinion processes converge to i.i.d. nonlinear Markov
(or McKean-Vlasov) processes; the limit opinion processes evolves as if under
the influence of opinions drawn from its own instantaneous law, which are the
unique solution of a nonlinear integro-differential equation of Kac type. This
implies that the (random) empirical distribution processes converges to this
(deterministic) solution. We then prove that, as time goes to infinity, this
solution converges to a law concentrated on isolated opinions too far apart to
interact, and identify sufficient conditions for the limit not to depend on the
initial condition, and to be concentrated at a single opinion. Finally, we
prove that if the equation has an initial condition with a density, then its
solution has a density at all times, develop a numerical scheme for the
corresponding functional equation, and show numerically that bifurcations may
occur.Comment: 43 pages, 7 figure
Agent Based Models and Opinion Dynamics as Markov Chains
This paper introduces a Markov chain approach that allows a rigorous analysis
of agent based opinion dynamics as well as other related agent based models
(ABM). By viewing the ABM dynamics as a micro description of the process, we
show how the corresponding macro description is obtained by a projection
construction. Then, well known conditions for lumpability make it possible to
establish the cases where the macro model is still Markov. In this case we
obtain a complete picture of the dynamics including the transient stage, the
most interesting phase in applications. For such a purpose a crucial role is
played by the type of probability distribution used to implement the stochastic
part of the model which defines the updating rule and governs the dynamics. In
addition, we show how restrictions in communication leading to the co-existence
of different opinions follow from the emergence of new absorbing states. We
describe our analysis in detail with some specific models of opinion dynamics.
Generalizations concerning different opinion representations as well as opinion
models with other interaction mechanisms are also discussed. We find that our
method may be an attractive alternative to mean-field approaches and that this
approach provides new perspectives on the modeling of opinion exchange
dynamics, and more generally of other ABM.Comment: 26 pages, 12 figure
On the modeling of neural cognition for social network applications
In this paper, we study neural cognition in social network. A stochastic
model is introduced and shown to incorporate two well-known models in Pavlovian
conditioning and social networks as special case, namely Rescorla-Wagner model
and Friedkin-Johnsen model. The interpretation and comparison of these model
are discussed. We consider two cases when the disturbance is independent
identical distributed for all time and when the distribution of the random
variable evolves according to a markov chain. We show that the systems for both
cases are mean square stable and the expectation of the states converges to
consensus.Comment: submitted to IEEE CCAT 201
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