Conservation laws and asymptotic behavior of a model of social dynamics. (English) Zbl 1132.91600
Summary: A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed by M.L. Bertotti and L. Delitala [Math. Models Methods Appl. Sci. 14, No. 7, 1061–1084 (2004; Zbl 1083.92032)]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions is investigated both analytically and computationally. Existence, stability and attractivity of certain equilibria are proved.
Keywords:
kinetic theory; discretization; Boltzmann models; population models; nonlinearity; asymptotic stabilityCitations:
Zbl 1083.92032References:
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