Boudin, Laurent; Salvarani, Francesco A kinetic approach to the study of opinion formation. (English) Zbl 1163.91537 ESAIM, Math. Model. Numer. Anal. 43, No. 3, 507 (2009). Summary: We use the methods of nonequilibrium statistical mechanics in order to derive an equation which models some mechanisms of opinion formation. After proving the main mathematical properties of the model, we provide some numerical results. Cited in 26 Documents MSC: 91D10 Models of societies, social and urban evolution 82C22 Interacting particle systems in time-dependent statistical mechanics Keywords:sociophysics; opinion formation; kinetic theory PDFBibTeX XMLCite \textit{L. Boudin} and \textit{F. Salvarani}, ESAIM, Math. Model. Numer. Anal. 43, No. 3, 507 (2009; Zbl 1163.91537) Full Text: DOI EuDML References: [1] G. Aletti, G. Naldi and G. Toscani, First-order continuous models of opinion formation. SIAM J. Appl. Math.67 (2007) 837-853 (electronic). Zbl1128.91043 · Zbl 1128.91043 [2] E. Ben-Naim, Opinion dynamics: rise and fall of political parties. Europhys. Lett.69 (2005) 671-677. [3] G.A. Bird, Molecular gas dynamics and the direct simulation of gas flows, Oxford Engineering Science Series42. The Clarendon Press, Oxford University Press, New York (1995). Corrected reprint of the 1994 original, Oxford Science Publications. [4] M. Campiti, G. Metafune and D. Pallara, Degenerate self-adjoint evolution equations on the unit interval. Semigroup Forum57 (1998) 1-36. Zbl0915.47029 · Zbl 0915.47029 [5] J.A. Carrillo, S. Cordier and G. Toscani, Over-populated tails for conservative in the mean, inelastic Maxwell models. Discrete Contin. Dyn. Syst. A (to appear). Available at . URIhttp://hal.archives-ouvertes.fr/hal-00206273/fr/ [6] S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy. J. Stat. Phys.120 (2005) 253-277. Zbl1133.91474 · Zbl 1133.91474 [7] G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents. Adv. Complex Systems3 (2000) 87-98. [8] M.R. Feix, D. Lepelley, V. Merlin and J.-L. Rouet, The probability of conflicts in a U.S. presidential type election. Econom. Theory23 (2004) 227-257. · Zbl 1128.91316 [9] S. Galam, Rational group decision making: A random field Ising model at t = 0 . Phys. A238 (1997) 66-80. [10] S. Galam, Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Phys. A333 (2004) 453-460. [11] S. Galam, Heterogeneous beliefs, segregation, and extremism in the making of public opinions. Phys. Rev. E71 (2005) 046123. [12] S. Galam and S. Moscovici, Towards a theory of collective phenomena: consensus and attitude changes in groups. Eur. J. Soc. Psychol.21 (1991) 49-74. [13] S. Galam and J.-D. Zucker, From individual choice to group decision-making. Phys. A287 (2000) 644-659. [14] S. Galam, Y. Gefen and Y. Shapir, Sociophysics: A new approach of sociological collective behaviour. I. Mean-behaviour description of a strike. J. Math. Sociol.9 (1982) 1-23. Zbl0496.92015 · Zbl 0496.92015 [15] R. Hegselmann and U. Krause, Opinion dynamics and bounded confidence: models, analysis and simulation. J. Artif. Soc. Soc. Sim.5 (2002). [16] F. Slanina, Inelastically scattering particles and wealth distribution in an open economy. Phys. Rev. E69 (2004) 046102. [17] F. Slanina and H. Lavicka, Analytical results for the Sznajd model of opinion formation. Eur. Phys. J. B35 (2003) 279-288. [18] K. Sznajd-Weron and J. Sznajd, Opinion evolution in closed community. Int. J. Mod. Phys. C11 (2000) 1157-1166. · Zbl 1146.82302 [19] G. Toscani, Kinetic models of opinion formation. Commun. Math. Sci.4 (2006) 481-496. · Zbl 1195.91128 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.