On the qualitative analysis of the solutions of a mathematical model of social dynamics

Abstract

This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061-1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.

Modelling opinion formation by means of kinetic equations

“…Nevertheless, they may be treated in the same way. Hence, the system which is eventually obtained now is very similar to (6). Indeed, if we denote by f 0 the density function for the political class, by f 1 and f 2 the ones for the electors respectively favouring party 1 and 2, by f 3 the one for nonvoting electors, and, again, by f = (f i ) 0≤i≤3 , Lo Schiavo can write, for any t, u and ν,…”

“…It is quite clear that the first Helbing model is a discrete velocity model. Note that this kind of model have been used later on to study opinion dynamics phenomena (for example, [6][7][8][9]). However, in the absence of spatial phenomena, their structure more remembers a dynamical system than a kinetic model.…”

From the discrete kinetic theory to modelling open systems of active particles

“…Paper [1] deals with a kinetic methodological approach where a class of evolution equations are proposed for modelling large systems of interacting individuals such that the microscopic state is a discrete variable; see also [2,3]. The aim for analyzing such systems is induced by modelling requirements rather than by the intention of reducing computational complexity.…”

Large Scale Daily Contacts and Mobility Model - an Individual-Based Countrywide Simulation Study for Poland

“…Applications of large-scale Monte Carlo type simulations aimed at mimicking a social context are not, of course, limited to the epidemiology alone. Ever since its inception over two decades ago (Galam 2004;Pabjan 2004) the interest in sociophysics, especially in modeling social dynamics (Bertotti andDelitala 2006 ,Ballas et al 2007) has grown considerably, spawning numerous sub-fields and their variants. Besides the epidemiology, macro-economical studies (Bai et al 2008 ) and supply-chain operational research ( Hammami et al 2008), two other areas share the requirement and the need for large scale simulations, namely, transportation systems and ecology (Beckmann et al 1996;Granger 2001;Hogeweg 2007).…”