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Modeling opinion formation in the kinetic theory of active particles I: spontaneous trend

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Abstract

The kinetic theory of active particles is used to model the formation and evolution of opinions in a structured population. The spatial structure is modeled by a network whose nodes mimic the geographic distribution of individuals, while the functional subsystems present in each node group together elements sharing a common orientation. In this paper we introduce a model, based on nonlinear and nonlinearly additive interactions among individuals, subsystems and nodes, related to the spontaneous evolution of opinion concerning given specific issues. Numerical solutions in a model situation not related with real data show how the mutual interactions are able to drive the subsystems opinion toward the emergence of collective structures characterizing this kind of complex systems.

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Notes

  1. Since it depends on more than 2 indexes, it is actually an array rather than a matrix.

  2. We recall that in this framework we label the subsystems and the nodes with integers. A possible alternative in the definition of the center of mass would consist in using the number of individuals \(n_{ij}(t)=\int _0^1f_{ij}(t,u)du\) in place of the distribution functions. In the context of opinion formation seems more reasonable keeping the definition (10).

  3. The center of mass does depend on the values of the functions appearing at the r.h.s. of (10), that is, the notation \(f(t,u^*)\) (say) stays for the value the function \(f\) assumes in correspondence of the values \(t\) and \(u^*\) of its arguments.

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  1. Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli 35, 44121 , Ferrara, Italy

    A. Benfenati & V. Coscia

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  1. A. Benfenati
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  2. V. Coscia
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Correspondence to V. Coscia.

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To Mariarosaria Padula, in memory.

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Benfenati, A., Coscia, V. Modeling opinion formation in the kinetic theory of active particles I: spontaneous trend. Ann Univ Ferrara 60, 35–53 (2014). https://doi.org/10.1007/s11565-014-0207-2

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