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On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim. (English) Zbl 1200.91258

Summary: This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.

MSC:

91D10 Models of societies, social and urban evolution
82C40 Kinetic theory of gases in time-dependent statistical mechanics
91A80 Applications of game theory

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[1] L. Arlotti and N. Bellomo, “Solution of a new class of nonlinear kinetic models of population dynamics,” Applied Mathematics Letters, vol. 9, no. 2, pp. 65-70, 1996. · Zbl 0853.35050 · doi:10.1016/0893-9659(96)00014-6
[2] L. Arlotti, N. Bellomo, and E. De Angelis, “Generalized kinetic (Boltzmann) models: mathematical structures and applications,” Mathematical Models & Methods in Applied Sciences, vol. 12, no. 4, pp. 567-591, 2002. · Zbl 1174.82325 · doi:10.1142/S0218202502001799
[3] L. Arlotti, N. Bellomo, and M. Lachowicz, “Kinetic equations modelling population dynamics,” Transport Theory and Statistical Physics, vol. 29, no. 1-2, pp. 125-139, 2000. · Zbl 1060.92029 · doi:10.1142/S0218202504003799
[4] L. Arlotti, N. Bellomo, and K. Latrach, “From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications,” Mathematical and Computer Modelling, vol. 30, no. 1-2, pp. 15-40, 1999. · Zbl 1043.92518 · doi:10.1016/S0895-7177(99)00113-2
[5] N. Bellomo and A. Bellouquid, “From a class of kinetic models to the macroscopic equations for multicellular systems in biology,” Discrete and Continuous Dynamical Systems. Series B, vol. 4, no. 1, pp. 59-80, 2004. · Zbl 0759.92011 · doi:10.1137/0152083
[6] N. Bellomo and A. Bellouquid, “On the onset of non-linearity for diffusion models of binary mixtures of biological materials by asymptotic analysis,” International Journal of Non-Linear Mechanics, vol. 41, no. 2, pp. 281-293, 2006. · Zbl 1043.92518 · doi:10.1016/S0895-7177(99)00113-2
[7] N. Bellomo, A. Bellouquid, and M. Delitala, “Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 11, pp. 1683-1733, 2004. · Zbl 0946.92019 · doi:10.1080/00411450008205864
[8] N. Bellomo and E. De Angelis, “Strategies of applied mathematics towards an immuno-mathematical theory on tumors and immune system interactions,” Mathematical Models & Methods in Applied Sciences, vol. 8, no. 8, pp. 1403-1429, 1998. · Zbl 0940.92032 · doi:10.1007/s002850050158
[9] N. Bellomo, M. Delitala, and V. Coscia, “On the mathematical theory of vehicular traffic flow. I. Fluid dynamic and kinetic modelling,” Mathematical Models & Methods in Applied Sciences, vol. 12, no. 12, pp. 1801-1843, 2002. · Zbl 1019.60064 · doi:10.1142/S0218202502002197
[10] N. Bellomo and M. Pulvirenti, Eds., Modeling in Applied Sciences. A Kinetic Theory Approach, N. Bellomo and M. Pulvirenti, Eds., Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Massachusetts, 2000. · Zbl 0938.00011 · doi:10.1016/j.mcm.2003.05.021
[11] A. Bellouquid, “On the asymptotic analysis of kinetic models towards the compressible Euler and acoustic equations,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 6, pp. 853-882, 2004. · Zbl 1067.91054 · doi:10.1016/S0898-1221(02)00221-3
[12] A. Bellouquid and M. Delitala, “Mathematical methods and tools of kinetic theory towards modelling complex biological systems,” Mathematical Models & Methods in Applied Sciences, vol. 15, no. 11, pp. 1639-1666, 2005. · Zbl 1062.91062 · doi:10.1016/S0895-7177(03)00005-0
[13] M. L. Bertotti and M. Delitala, “From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 7, pp. 1061-1084, 2004. · Zbl 1083.92032 · doi:10.1142/S0218202504003544
[14] H. Bessaih and F. Flandoli, “Limit behaviour of a dense collection of vortex filaments,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 2, pp. 189-215, 2004. · Zbl 1010.91088 · doi:10.1016/S0378-4371(02)01582-0
[15] B. Carbonaro and C. Giordano, “A second step towards a stochastic mathematical description of human feelings,” Mathematical and Computer Modelling, vol. 41, no. 4-5, pp. 587-614, 2005. · Zbl 1116.91074 · doi:10.1016/j.mcm.2003.05.021
[16] B. Carbonaro and N. Serra, “Towards mathematical models in psychology: a stochastic description of human feelings,” Mathematical Models & Methods in Applied Sciences, vol. 12, no. 10, pp. 1453-1490, 2002. · Zbl 1019.60064 · doi:10.1142/S0218202502002197
[17] M. Delitala, “Nonlinear models of vehicular traffic flow-new frameworks of the mathematical kinetic theory,” Comptes Rendus Mecanique, vol. 331, no. 12, pp. 817-822, 2003. · Zbl 0947.92014 · doi:10.1142/S0218202598000664
[18] L. Derbel, “Analysis of a new model for tumor-immune system competition including long-time scale effects,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 11, pp. 1657-1681, 2004. · Zbl 1057.92036 · doi:10.1142/S0218202504003738
[19] F. Filbet, P. Lauren\ccot, and B. Perthame, “Derivation of hyperbolic models for chemosensitive movement,” Journal of Mathematical Biology, vol. 50, no. 2, pp. 189-207, 2005. · Zbl 0713.92018 · doi:10.1007/BF00277392
[20] S. Galam, “Modelling rumors: the no plane Pentagon French hoax case,” Physica A: Statistical Mechanics and Its Applications, vol. 320, no. 1-4, pp. 571-580, 2003. · Zbl 1010.91088 · doi:10.1016/S0378-4371(02)01582-0
[21] S. Galam, “Contrarian deterministic effects on opinion dynamics: “the hung elections scenario”,” Physica A: Statistical Mechanics and Its Applications, vol. 333, no. 1-4, pp. 453-460, 2004. · Zbl 1137.76387 · doi:10.1142/S0218202504003209
[22] S. Galam, “Sociophysics: a personal testimony,” Physica A: Statistical and Theoretical Physics, vol. 336, no. 1-2, pp. 49-55, 2004. · Zbl 1149.76654 · doi:10.1142/S0218202504003702
[23] K. P. Hadeler, T. Hillen, and F. Lutscher, “The Langevin or Kramers approach to biological modeling,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 10, pp. 1561-1583, 2004. · Zbl 1057.92012 · doi:10.1142/S0218202504003726
[24] D. Helbing, “Traffic and related self-driven many-particle systems,” Reviews of Modern Physics, vol. 73, no. 4, pp. 1067-1141, 2001. · Zbl 1223.82042 · doi:10.1016/j.crme.2003.09.008
[25] E. Jäger and L. A. Segel, “On the distribution of dominance in populations of social organisms,” SIAM Journal on Applied Mathematics, vol. 52, no. 5, pp. 1442-1468, 1992. · Zbl 1041.76061 · doi:10.1142/S0218202502002343
[26] M. Lachowicz, “Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours,” Mathematical Models & Methods in Applied Sciences, vol. 15, no. 11, pp. 1667-1683, 2005. · Zbl 0938.00011
[27] P.-L. Lions and N. Masmoudi, “From the Boltzmann equations to the equations of incompressible fluid mechanics. I,” Archive for Rational Mechanics and Analysis, vol. 158, no. 3, pp. 173-193, 2001. · Zbl 0853.35050 · doi:10.1016/0893-9659(96)00014-6
[28] M. Lo Schiavo, “Population kinetic models for social dynamics: dependence on structural parameters,” Computers & Mathematics with Applications, vol. 44, no. 8-9, pp. 1129-1146, 2002. · Zbl 1067.91054 · doi:10.1016/S0898-1221(02)00221-3
[29] M. Lo Schiavo, “The modelling of political dynamics by generalized kinetic (Boltzmann) models,” Mathematical and Computer Modelling, vol. 37, no. 3-4, pp. 261-281, 2003. · Zbl 0987.76088 · doi:10.1007/s002050100144
[30] A. Mogilner and L. Edelstein-Keshet, “A non-local model for a swarm,” Journal of Mathematical Biology, vol. 38, no. 6, pp. 534-570, 1999. · Zbl 0940.92032 · doi:10.1007/s002850050158
[31] H. G. Othmer, S. R. Dunbar, and W. Alt, “Models of dispersal in biological systems,” Journal of Mathematical Biology, vol. 26, no. 3, pp. 263-298, 1988. · Zbl 0713.92018 · doi:10.1007/BF00277392
[32] T. Platkowski, “Evolution of populations playing mixed multiplayer games,” Mathematical and Computer Modelling, vol. 39, no. 9-10, pp. 981-989, 2004. · Zbl 1057.92012 · doi:10.1142/S0218202504003726
[33] F. Schweitzer, Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences, Springer Series in Synergetics, Springer, Berlin, 2003. · Zbl 1044.92021 · doi:10.3934/dcdsb.2004.4.59
[34] T. Vicsek, “A question of scale,” Nature, vol. 411, no. 6836, p. 421, 2001. · Zbl 1078.92036 · doi:10.1142/S0218202505000935
[35] M. Willander, E. Mamontov, and Z. Chiragwandi, “Modelling living fluids with the subdivision into the components in terms of probability distributions,” Mathematical Models & Methods in Applied Sciences, vol. 14, no. 10, pp. 1495-1520, 2004. · Zbl 1149.76654 · doi:10.1142/S0218202504003702
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