Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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The Dynamics of the Economic Evolution with the Capital Depreciation

Author(s):

Alexander Nikolajevich Kirillov

Federal Research Center "Karelian Research Center of the Russian Academy of Sciences"
185910, Petrozavodsk, Pushkinskaya ul., 11
Institute of Applied Mathematical Research
Dr. Sci. in Physics and Mathematics, Associate Professor

kirillov@krc.karelia.ru

Alexander Mihaylovich Sazonov

Federal Research Center "Karelian Research Center of the Russian Academy of Sciences"
185910, Petrozavodsk, Pushkinskaya ul., 11
Institute of Applied Mathematical Research
Postgraduate student

sazon-tb@mail.ru

Abstract:

The mathematical model of sector capital distribution dynamics over efficiency levels with the depreciation is proposed. The qualitative analysis of the model is presented. The globally stable set (attractor) is constructed. The equilibria of the proposed dynamical model are determined, in the case of two efficiency levels their global stability is proved. It is shown that the global stability of the equilibrium means that the depreciation process causes excess production. It is proved that in the case of three efficiency levels there exists a unique equilibrium. In the case without the capital migrating from the second level to the first one the global stability of the equilibrium is proved.

Keywords

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