Abstract
We study a mathematical model of abstract society with redistribution of the social energy of individuals determined by two factors, namely, by the mutual competition and the presence of external influence. The behavior of the analyzed model is described by relatively simple iterative equations generating a dynamic system with discrete time. Fixed points of the system are determined. For some of these points that are attractors, their pools are partially described. In the general case, we prove the convergence of trajectories to the equilibrium states. In particular, it is shown that the individuals with the highest initial energy are doomed to be defeated if one of weaker individuals receives a sufficiently strong external support. Four examples are discussed to illustrate the most interesting cases of external influence on the dynamics of competition between individuals in an abstract society.
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