Opinion dynamics over complex networks: kinetic modeling and numerical methods

site_artGiacomo Albi, Lorenzo Pareschi, Mattia Zanella

(31/03/2016 arxiv.org/abs/1604.00421)

In this paper we consider the modeling of opinion dynamics over time
dependent large scale networks. A kinetic description of the agents’
distribution over the evolving network is considered which combines an opinion
update based on binary interactions between agents with a dynamic creation and
removal process of new connections. The number of connections of each agent
influences the spreading of opinions in the network but also the way
connections are created is influenced by the agents’ opinion. The evolution of
the network of connections is studied by showing that its asymptotic behavior
is consistent both with Poisson distributions and truncated power-laws. In
order to study the large time behavior of the opinion dynamics a mean field
description is derived which allows to compute exact stationary solutions in
some simplified situations. Numerical methods which are capable to describe
correctly the large time behavior of the system are also introduced and
discussed. Finally, several numerical examples showing the influence of the
agents’ number of connections in the opinion dynamics are reported.

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