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Asymptotic analysis of continuous opinion dynamics models under bounded confidence

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  • This paper deals with the asymptotic behavior of mathematical models for opinion dynamics under bounded confidence of Deffuant-Weisbuch type. Focusing on the Cauchy Problem related to compromise models with homogeneous bound of confidence, a general well-posedness result is provided and a systematic study of the asymptotic behavior in time of the solution is developed. More in detail, we prove a theorem that establishes the weak convergence of the solution to a sum of Dirac masses and characterizes the concentration points for different values of the model parameters. Analytical results are illustrated by means of numerical simulations.
    Mathematics Subject Classification: Primary: 35R09, 35B40; Secondary: 91D10.


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  • [1]

    G. Aletti, G. Naldi and G. Toscani, First-order continuous models of opinion formation, SIAM J. Appl. Math., 67 (2007), 837-853.doi: 10.1137/060658679.


    A. Baldassarri, U. Marini Bettolo Marconi and A. Puglisi, Kinetic models of inelastic gases, Mat. Mod. Meth. Appl. Sci., 12 (2002), 965-983.doi: 10.1142/S0218202502001982.


    E. Ben-Naim, P. L. Krapivsky and S. Redner, Bifurcation and patterns in compromise processes, Phys. D, 183 (2003), 190-204.doi: 10.1016/S0167-2789(03)00171-4.


    M. L. Bertotti, On a class of dynamical systems with emerging cluster structure, Jour. Diff. Eq., 249 (2010), 2757-2770.doi: 10.1016/j.jde.2010.03.014.


    V. Blondel, J. M. Hendrickx and J. N. Tsitsiklis, On the $2R$ conjecture for multiagent systems, Proc. Europ. Control Conf., Kos, Greece, (2007), 874-881.


    L. Boudin and F. Salvarani, Modelling opinion formation by means of kinetic equations, in "Mathematical Modeling of Collective Behavior in Socio-economic and Life Sciences" (G. Naldi, L. Pareschi and G. Toscani eds.), (2010), 245-270, Birkhauser, Boston.doi: 10.1007/978-0-8176-4946-3_10.


    L. Boudin and F. Salvarani, The quasi-invariant limit for a kinetic model of sociological collective behavior, Kinet. Relat. Models, 2 (2009) 433-449.doi: 10.3934/krm.2009.2.433.


    L. Boudin and F. Salvarani, A kinetic approach to the study of opinion formation, M2AN Math. Model. Numer. Anal., 43 (2009), 507-522.doi: 10.1051/m2an/2009004.


    C. Canuto, F. Fagnani and P. Tilli, A Eulerian approach to the analysis of rendez-vous algorithms, Proc. of 2008 IFAC Conf., (2008), 9039-9044.


    G. Como and F. Fagnani, Scaling limits for continuous opinion dynamics systems, Ann. Appl. Probab., 21 (2011), 1537-1567.doi: 10.1214/10-AAP739.


    S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, Journal of Statistical Physics, 120 (2005), 253-277.doi: 10.1007/s10955-005-5456-0.


    G. Deffuant, D. Neau, F. Amblard and G. Weisbuch, Mixing beliefs among interacting agents, Adv. Comp. Sys., 3 (2001), 87-98.doi: 10.1142/S0219525900000078.


    B. Düring, P. Markowich, J-F. Pietschmann and M-T.Wolfram, Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders, Proc. R. Soc. Lond. A, 465 (2009)(2112), 3687-3708.doi: 10.1098/rspa.2009.0239.


    S. Galam, A review of Galam models, Int. J. Mod. Phys. C, 409 (2008), 3687-3708.


    U. Krause, A discrete nonlinear and non-autonomous model of consensus formation, in "Communications in Difference Equations" (S. Elaydi, G. Ladas, J. Popenda and J. Rakowski eds.), Gordon and Breach Science Publ., Amsterdam, (2000) 227-236.


    J. Lorenz, A stabilization theorem for continuous opinion dynamics, Phys. A, 355 (2005), 217-223.doi: 10.1016/j.physa.2005.02.086.


    J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, Internat. J. Modern Phys. C, 18 (2007), 1819-1838.doi: 10.1142/S0129183107011789.


    S. McNamara and W. R. Young, Kinetics of a one dimensional granular medium in the quasi elastic limit, Phys. Fluids A, 5 (1993), 34-45.doi: 10.1063/1.858896.


    L. Pareschi and G. Toscani, Self-similarity and power-like tails in nonconservative kinetic models, J. Stat. Phys., 124 (2006), 747-779.doi: 10.1007/s10955-006-9025-y.


    G. Toscani, Kinetic models of opinion formation, Commun. Math. Sci., 4 (2006), 481-496.


    G. Weisbuch, G. Deffuant, F. Amblard and J. P. Nadal, Meet, discuss, and segregate!, Complexity, 7 (2002), 55-63.doi: 10.1002/cplx.10031.

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