Networks and Heterogeneous Media (NHM)

Modeling opinion dynamics: How the network enhances consensus

Pages: 877 - 896, Volume 10, Issue 4, December 2015      doi:10.3934/nhm.2015.10.877

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Marina Dolfin - Dep. of Civil, Computer, Construction, Environmental Engineering and of Applied Mathematics (DICIEAMA), University of Messina, Contrada Di Dio Vill. S. Agata, Messina, Italy (email)
Mirosław Lachowicz - Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland (email)

Abstract: In this paper we analyze emergent collective phenomena in the evolution of opinions in a society structured into few interacting nodes of a network. The presented mathematical structure combines two dynamics: a first one on each single node and a second one among the nodes, i.e. in the network. The aim of the model is to analyze the effect of a network structure on a society with respect to opinion dynamics and we show some numerical solutions addressed in this direction, i.e. comparing the emergent behaviors of a consensus-dissent dynamic on a single node when the effect of the network is not considered, with respect to the emergent behaviors when the effect of a network structure linking few interacting nodes is considered. We adopt the framework of the Kinetic Theory for Active Particles (KTAP), deriving a general mathematical structure which allows to deal with nonlinear features of the interactions and representing the conceptual framework toward the derivation of specific models. A specific model is derived from the general mathematical structure by introducing a consensus-dissent dynamics of interactions and a qualitative analysis is given.

Keywords:  Active particles, opinion dynamics, nonlinear interactions, network.
Mathematics Subject Classification:  Primary: 91B15, 91B74, 35Q91; Secondary: 35R06.

Received: November 2014;      Revised: May 2015;      Available Online: October 2015.