48,495 research outputs found
Hydrodynamic models of preference formation in multi-agent societies
In this paper, we discuss the passage to hydrodynamic equations for kinetic
models of opinion formation. The considered kinetic models feature an opinion
density depending on an additional microscopic variable, identified with the
personal preference. This variable describes an opinion-driven polarisation
process, leading finally to a choice among some possible options, as it happens
e.g. in referendums or elections. Like in the kinetic theory of rarefied gases,
the derivation of hydrodynamic equations is essentially based on the
computation of the local equilibrium distribution of the opinions from the
underlying kinetic model. Several numerical examples validate the resulting
model, shedding light on the crucial role played by the distinction between
opinion and preference formation on the choice processes in multi-agent
societies.Comment: 30 pages, 15 figure
Opinion modeling on social media and marketing aspects
We introduce and discuss kinetic models of opinion formation on social
networks in which the distribution function depends on both the opinion and the
connectivity of the agents. The opinion formation model is subsequently coupled
with a kinetic model describing the spreading of popularity of a product on the
web through a social network. Numerical experiments on the underlying kinetic
models show a good qualitative agreement with some measured trends of hashtags
on social media websites and illustrate how companies can take advantage of the
network structure to obtain at best the advertisement of their products
Boltzmann type control of opinion consensus through leaders
The study of formations and dynamics of opinions leading to the so called
opinion consensus is one of the most important areas in mathematical modeling
of social sciences. Following the Boltzmann type control recently introduced in
[G. Albi, M. Herty, L. Pareschi arXiv:1401.7798], we consider a group of
opinion leaders which modify their strategy accordingly to an objective
functional with the aim to achieve opinion consensus. The main feature of the
Boltzmann type control is that, thanks to an instantaneous binary control
formulation, it permits to embed the minimization of the cost functional into
the microscopic leaders interactions of the corresponding Boltzmann equation.
The related Fokker-Planck asymptotic limits are also derived which allow to
give explicit expressions of stationary solutions. The results demonstrate the
validity of the Boltzmann type control approach and the capability of the
leaders control to strategically lead the followers opinion
The size distribution of cities: a kinetic explanation
We present a kinetic approach to the formation of urban agglomerations which
is based on simple rules of immigration and emigration. In most cases, the
Boltzmann-type kinetic description allows to obtain, within an asymptotic
procedure, a Fokker--Planck equation with variable coefficients of diffusion
and drift, which describes the evolution in time of some probability density of
the city size. It is shown that, in dependence of the microscopic rules of
migration, the equilibrium density can follow both a power law for large values
of the size variable, which contains as particular case a Zipf's law behavior,
and a lognormal law for middle and low values of the size variable. In
particular, connections between the value of Pareto index of the power law at
equilibrium and the disposal of the population to emigration are outlined. The
theoretical findings are tested with recent data of the populations of Italy
and Switzerland
Kinetic models of opinion formation
We introduce and discuss certain kinetic models of (continuous) opinion
formation involving both exchange of opinion between individual agents and
diffusion of information. We show conditions which ensure that the kinetic
model reaches non trivial stationary states in case of lack of diffusion in
correspondence of some opinion point. Analytical results are then obtained by
considering a suitable asymptotic limit of the model yielding a Fokker-Planck
equation for the distribution of opinion among individuals
- …