Modeling opinion dynamics: How the network enhances consensus
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) 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 consensusdissent 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 consensusdissent dynamics of interactions and a qualitative analysis is given.
Keywords: Active particles, opinion dynamics, nonlinear interactions, network.
Received: November 2014; Revised: May 2015; Available Online: October 2015. 
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