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Quality & Quantity

, Volume 41, Issue 4, pp 545–555 | Cite as

From the kinetic theory of active particles to the modeling of social behaviors and politics

  • Nicola Bellomo
  • Maria Letizia Bertotti
  • Marcello Delitala
Original Paper

Abstract

This paper deals with the modeling of complex social systems by methods of the mathematical kinetic theory for active particles. Specifically, a recent model by the last two authors is analyzed from the social sciences point of view. The model shows, despite its simplicity, some interesting features. In particular, this paper investigates the ability of the model to describe how a social politics and the disposable overall wealth may have a relevant influence towards the trend of the wealth distribution. The paper also outlines various research perspectives.

Keywords

Complexity Kinetic theory Nonlinearity Social systems Active particles 

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References

  1. Arlotti L., Bellomo N. and Latrach K. (1999). From the Jäger and Segel model to kinetic population dynamics: nonlinear evolution problems and applications. Math. Comp. Model. 30: 15–40 CrossRefGoogle Scholar
  2. Bellomo N. and Forni G. (2006). Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Math. Mod. Meth. Appl. Sci 16: 1001–1029 CrossRefGoogle Scholar
  3. Bellomo N. and Carbonaro B. (2006). On the modelling of complex socio-psychological systems with some reasoning about Kate, Jules and Jim. Diff. Equations Nonlinear Mech. 1: 1–26 CrossRefGoogle Scholar
  4. Bellomo N. (2007). Modelling Complex Living Systems by Kinetic Theory Approach. Birkäuser, Boston Google Scholar
  5. Bellouquid A. and Delitala M. (2005). Mathematical tools towards modelling complex systems by the kinetic theory approach. Math. Mod. Meth. Appl. Sci. 15: 1639–1666 CrossRefGoogle Scholar
  6. Bellouquid A. and Delitala M. (2006). Mathematical Modeling of Complex Biological Systems. A Kinetic Theory Approach. Birkäuser, Boston Google Scholar
  7. Bertotti M.L. and Delitala M. (2004). From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences. Math. Mod. Meth. Appl. Sci. 14: 1061–1084 CrossRefGoogle Scholar
  8. Bertotti M.L. and Delitala M. (2006). On the qualitative analysis of the solutions of a mathematical model of social dynamics. Appl. Math. Lett. 19: 1107–1112 CrossRefGoogle Scholar
  9. Bertotti M.L., Delitala M.: Conservation laws and asymptotic behavior of a model of social dynamics. Nonlinear Anal. Real World Appl. (2007), in printGoogle Scholar
  10. Carbonaro B. and Serra N. (2002). Towards mathematical models in psychology: a stochastic description of human feelings. Math. Mod. Meth. Appl. Sci. 12: 1463–1498 CrossRefGoogle Scholar
  11. Chauviere A. and Brazzoli I. (2006). On the discrete kinetic theory for active particles. Mathematical tools. Math. Comp. Model. 43: 933–944 CrossRefGoogle Scholar
  12. Galam S. (2003). Contrarian deterministic effects on opinion dynamics: the hung elections scenario. Physica A 333: 453–460 CrossRefGoogle Scholar
  13. El Ghordaf J. and Hbid M. L. (2006). Mathematical analysis of the evolution of a model of regional population distribution. Math. Mod. Meth. Appl. Sci. 16: 347–374 CrossRefGoogle Scholar
  14. Hogeweg P. and Hesper P. (1983). The ontogeny of the interaction structure in bumble bee colonies. Behav. Ecol. Sociobiol. 12: 271–283 CrossRefGoogle Scholar
  15. Hughes R.L. (2003). The flow of human crowds. Ann. Rev. Fluid Mech. 35: 169–182 CrossRefGoogle Scholar
  16. Jäger E. and Segel L. (1992). On the distribution of dominance in populations of social organisms. SIAM J. Appl. Math. 52: 1442–1468 CrossRefGoogle Scholar
  17. May R.M. (2004). Uses and abuses of mathematics in biology. Science 303: 790–793 CrossRefGoogle Scholar
  18. Reed R. (2004). Why is mathematical biology so hard?. Notices Am. Math. Soc 11: 338–342 Google Scholar
  19. Tabata M., Eshima N. and Takagi I. (2006). A geometrical similarity between migration of human population and diffusion of biological particles. Nonlinear Anal. Real World Appl. 7: 872–894 CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  • Nicola Bellomo
    • 1
  • Maria Letizia Bertotti
    • 2
  • Marcello Delitala
    • 1
  1. 1.Dipartimento di MatematicaPolitecnicoTorinoItaly
  2. 2.Dipartimento di Metodi e Modelli MatematiciUniversità di PalermoPalermoItaly

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