Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 9, Issue 1, Pages 183-196Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2006.09.012
Keywords
kinetic theory; discretization; Boltzmann models; population models; nonlinearity; asymptotic stability
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A conservative social dynamics model is developed within a discrete kinetic framework for active particles. which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061-1084]. 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. (c) 2006 Elsevier Ltd. All rights reserved.
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