Subject: [ SHS.SOCIO ] Humanities and Social Sciences/Sociology | [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP] | opinion formation | Sociophysics | [SHS.SOCIO]Humanities and Social Sciences/Sociology | kinetic theory | [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophy... View more
1. G. Aletti, G. Naldi, and G. Toscani. First-order continuous models of opinion formation. SIAM J. Appl. Math., 67(3):837-853 (electronic), 2007.
2. L. Arlotti, N. Bellomo, and E. De Angelis. Generalized kinetic (Boltzmann) models: mathematical structures and applications. Math. Models Methods Appl. Sci., 12(4):567-591, 2002.
3. E. Ben-Naim. Opinion dynamics: rise and fall of political parties. Europhys. Lett., 69:671-677, 2005.
4. E. Ben-Naim, P. L. Krapivsky, and S. Redner. Bifurcation and patterns in compromise processes. Phys. D, 183(3-4):190-204, 2003.
5. E. Ben-Naim, P. L. Krapivsky, F. Vazquez, and S. Redner. Unity and discord in opinion dynamics. Phys. A, 330(1-2):99-106, 2003. Randomness and complexity (Eilat, 2003).
6. M.-L. Bertotti and M. Delitala. On the qualitative analysis of the solutions of a mathematical model of social dynamics. Appl. Math. Lett., 19(10):1107-1112, 2006.
7. M.-L. Bertotti and M. Delitala. Conservation laws and asymptotic behavior of a model of social dynamics. Nonlinear Anal. Real World Appl., 9(1):183-196, 2008.
8. M.-L. Bertotti and M. Delitala. On a discrete generalized kinetic approach for modelling persuader's influence in opinion formation processes. Math. Comput. Modelling, 48(7-8):1107-1121, 2008.
9. M.-L. Bertotti and M. Delitala. On the existence of limit cycles in opinion formation processes under time periodic influence of persuaders. Math. Models Methods Appl. Sci., 18(6):913-934, 2008.
10. G.A. Bird. Molecular gas dynamics and the direct simulation of gas flows, volume 42 of Oxford Engineering Science Series. The Clarendon Press Oxford University Press, New York, 1995. Corrected reprint of the 1994 original.