KINETIC MODELS OF OPINION FORMATION

Communications in Mathematical Sciences

Volumn 4, Issue 3, 2006, Pages 481-496

  Toscani, Giuseppe ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

Boltzmann equation; Opinion formation; Sociophysics

Indexed keywords

EID: 34547461832     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2006.v4.n3.a1     Document Type: Article

References (30)

1. [1] E. Ben-Naim, Opinion dynamics: rise andfall ofpolitical parties, Europhys. Lett., 69, 671-677,2005.
2. [2] E. Ben-Naim, P. L. Krapivski and S. Redner, Bifurcations and patterns in compromise pro-cesses, Physica D, 183, 190-204, 2003.
3. [3] E. Ben-Naim, P. L. Krapivski, R. Vazquez and S. Redner, Unity and discord in opinion dy-namics, Physica A, 330, 99-106, 2003.
4. [4] A. V. Bobylev, The theory of the spatially uniform Boltzmann equation for Maxwell molecules,Sov. Sci. Review C, 7, 112-233, 1988.
5. [5] J. P. Bouchaud and M. Mézard, Wealth condensation in a simple model of economy, Physica A, 282, 536-545, 2000.
6. [6] C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer Series in Applied Mathematical Sciences, Springer—Verlag, 106, 1994.
7. [7] S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, J.Statist. Phys., 120, 253-277, 2005.
8. [8] G. Deffuant, F. Amblard, G. Weisbuch and T. Faure, How can extremism prevail? A study based on the relative agreement interaction model, JASSS J. Art. Soc. Sim., 5, 4, 2002.
9. [9] P. Degond, L. Pareschi and G. Russo, Modelling and Numerical Methods for Kinetic Equations,Birkhauser, 2004.
10. [10] S. Fortunato, Monte Carlo simulations of opinion dynamics, cond-mat/0501105.
11. [11] S. Galam, Y. Gefen and Y. Shapir, Sociophysics: a new approach of sociological collective behavior, J. Math. Sociology, 9, 1-13, 1982.
12. [12] R. Hegselman and U. Krause, Opinion dynamics and bounded confidence models, analysis, and simulation, JASSS J. Art. Soc. Soc. Sim., 5, 3, 2002.
13. [13] A. Klar and R. Wegener, A kinetic model for vehicular traffic derived from a stochastic microscopic model, Transp. Theory Stat. Phys., 25(7), 785-798, 1996.
14. [14] R. G. Laha and V. K. Rohatgi, Probability Theory, John Wiley and Sons, New York, 1979.
15. [15] T. M. Liggett, Stochastic Interacting Systems: Contact, Voter, and Exclusion Processes, Springer Verlag, Berlin, 1999.
16. [16] O. Malcai, O. Biham, S. Solomon and P. Richmond, Theoretical analysis and simulations ofthe generalized Lotka-Volterra model, Phys. Rev. E, 66, 031-102, 2002.
17. [17] S. McNamara and W. R. Young, Kinetics of a one-dimensional granular medium in the quasi-elastic limit, Phys. Fluids A, 5, 34-45, 1993.
18. [18] R. Ochrombel, Simulation of Sznajd sociophysics model with convincing single opinions, Int.J. Mod. Phys. C, 12, 1091-1092, 2001.
19. [19] V. Pareto, Cours d'Economie Politique, Lausanne and Paris, 1897.
20. [20] W. Rash, Politics on the nets: Wiring the Political Process, Freeman, New York, 1997.
21. [21] F. Slanina, Inelastically scattering particles and wealth distribution in an open economy, Phys.Rev. E, 69, 046-102, 2004.
22. [22] F. Slanina, H. Lavicka, Analytical results for the Sznajd model of opinion formation, Eur. Phys.J. B, 35, 279-288, 2003.
23. [23] S. Solomon, Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generi-cally to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes, Computational Finance 97, eds. A-P. N. Refenes, A. N. Burgess, J. E. Moody, Kluwer Academic Publishers, 1998.
24. [24] D. Stauffer, Percolation and Galam theory of minority opinion spreading, Int. J. Mod. Phys.C, 13, 315-318, 2002.
25. [25] D. Stauffer and P. M. C. Oliveira, Persistence of opinion in the Sznajd consensus model:computer simulation, Eur. Phys. J. B, 30, 587-592, 2002.
26. [26] D. Stauffer and H. Meyer-Ortmanns, Simulation of consensus model of deftuant et al. on a Barabasi-Albert network, Int. J. Mod. Phys. B, 15, 241-246, 2004.
27. [27] K. Sznajd-Weron and J. Sznajd, Opinion evolution in closed community, Int. J. Mod. Phys.C, 11, 1157-1166, 2000.
28. [28] G. Toscani, One-dimensional kinetic models of granular flows, RAIRO Modél Math. Anal.Numér., 34, 1277-1291, 2000.
29. [29] W. Weidlich, Sociodynamics: A Systematic Approach To Mathematical Modelling In The SocialSciences, Harwood Academic Publishers, 2000.
30. [30] G. Weisbuch, G. Deffuant, F. Amblard and J. P. Nadal, Meet, discuss, and segregate!, Com-plexity, 7, 55-63, 2002.