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Modeling dynamics of sustainable environmental and economic development of closed territorial formations

Keywords:

M.E. Semenov – Dr.Sc. (Phys.-Math.), Professor, 11 Department of Theoretical Hydrometeorology, Military Educational Research Centre of Air Force «Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh). E-mail: mkl150@mail.ru
V.V. Koida – Postgraduate Student, 11 Department of Theoretical Hydrometeorology, Military Educational Research Centre of Air Force «Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh). E-mail: VVKoida@yandex.ru
M.O. Gedzenko – Postgraduate Student, Department of Mathematics, Voronezh GASU. E-mail: MOGEDZ@mail.ru
A.V. Samsonov – Postgraduate Student, 11 Department of Theoretical Hydrometeorology, Military Educational Research Centre of Air Force «Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh). E-mail: Sinoptik78@mail.ru


Main provisions of the mathematical model of ecological and economic development territorial entities: production function sets the correspondence between involvement in the production process of capital, reproducible and non-renewable natural resources, on the one hand, and the release of a "composite" of the product – on the other. The term "composite" refers to the product generated in the production process the material substance capable, due to its properties as participate in the nonproductive consumption and in the production process as the capital production and, furthermore, – the reproduced as a natural resource; there is a substitution between the production and the result of natural renewable resources (mediated in the real economy cleaning process). Taking the concept of a composite product that combines the functions of production and purification, which simplifies further analysis; in the considered time interval, it is possible to aggregate different types of capital, and non-renewable natural renewable resources in scalar quantities, respectively; the depreciation rate of capital is assumed constant; accepted assumptions about the constancy in time by any amount and structure of the labor force; known value of stocks of non-renewable natural resources and the state played in the initial time. Possibility of direct interchanging between them is eliminated; the production function is homogeneous of the first order, concave, continuous and differentiable on the set of their arguments; reduction coefficient at different times of economic indicators change over time. Under the assumptions made on the equation describing the economic system imposed an additional condition on the return of the "composite" of the product (as reproduced environmental benefits) in the environment. The model is formulated in terms of optimal control problems, the analysis of the model is performed using the maximum principle L.S. Pontryagin.
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