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Matem. Mod., 2012, Volume 24, Number 2, Pages 120–128 (Mi mm3210)  

This article is cited in 5 scientific papers (total in 5 papers)

The “power-society-economy” model with a slightly corrupt discrete hierarchy

M. G. Dmitrievab, A. A. Pavlova, A. P. Petrovcd

a Institute of Systems Analysis, Russian Academy of Sciences
b National Research University "Higher School of Economics"
c M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
d Lomonosov Moscow State University, Faculty of Sociology

Abstract: For the “power-society-economy” discrete chain model in the case of a slightly corrupt hierarchy the problem of finding the distribution of power, maximizing per capita consumption in steady state is considered. This problem reduces to finding the maximum of a nonlinear function of many variables with a small parameter and linear constraints. With the help of the asymptotic expansion of the objective function has constructed a linear programming problem to determine the terms of the asymptotic of the first order. The obtained extreme problems lead to an approximate stationary distribution of power maximizing per capita consumption. An illustrative example is given.

Keywords: “power-society-economics model”, linear programming, small parameter, asymptotic expansion.

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Received: 20.06.2011

Citation: M. G. Dmitriev, A. A. Pavlov, A. P. Petrov, “The “power-society-economy” model with a slightly corrupt discrete hierarchy”, Matem. Mod., 24:2 (2012), 120–128

Citation in format AMSBIB
\Bibitem{DmiPavPet12}
\by M.~G.~Dmitriev, A.~A.~Pavlov, A.~P.~Petrov
\paper The ``power-society-economy'' model with a slightly corrupt discrete hierarchy
\jour Matem. Mod.
\yr 2012
\vol 24
\issue 2
\pages 120--128
\mathnet{http://mi.mathnet.ru/mm3210}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2977123}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Petrov, M. E. Stepantsov, “Diskretnaya raspredelennaya modifikatsiya modeli vlastobschestvo na osnove kletochnogo avtomata”, Preprinty IPM im. M. V. Keldysha, 2014, 100, 19 pp.  mathnet
    2. A. P. Petrov, M. E. Stepantsov, “Modelirovanie trekhurovnevoi sistemy vlast-obschestvo na osnove kletochnykh avtomatov”, Matem. modelirovanie, 28:3 (2016), 119–132  mathnet  elib
    3. M. E. Stepantsov, “Diskretnaya matematicheskaya model sistemy «vlast-obschestvo-ekonomika» na osnove kletochnogo avtomata”, Kompyuternye issledovaniya i modelirovanie, 8:3 (2016), 561–572  mathnet  crossref
    4. M. E. Stepantsov, “Simulation of “power-society-economics” system with elements of corruption based on cellular automata”, Math. Models Comput. Simul., 10:2 (2018), 249–254  mathnet  crossref  elib
    5. V. I. Kachalov, “On one method of solving singularly perturbed systems of Tikhonov's type”, Russian Math. (Iz. VUZ), 62:6 (2018), 21–26  mathnet  crossref  isi
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