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Volume 61 >>> № 6 NOVEMBER — DECEMBER 2025

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UDC 517.9

K.L. Atoyev
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, konstantin_atoyev@yahoo.com

P.S. Knopov
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, knopov1@yahoo.com

MATHEMATICAL MODELING OF INSTABILITY IN ECOLOGICAL
AND ECONOMIC SYSTEMS

Abstract. The study of the mechanisms underlying the instability of complex ecological-economic systems was conducted to identify effective strategies for managing the energy sector of the economy in the context of climate change. The work uses a six-sector Lorenz model with variable coefficients, which combines in a single structure the sectors of the economy described in the same way, each of which is considered in terms of productivity levels, the number of jobs, and structural violations. The model allows us to investigate how changes in the ratio of demand and supply in individual industries and the speed of eliminating violations in the ecological-economic systems affect the share of green energy in the energy balance, the total volume of greenhouse gas emissions and energy production, and the number of structural disturbances in all sectors of the economy. The conditions for the occurrence of instability in complex ecological-economic systems associated with turbulent regimes, which lead to an increase in the total number of structural disturbances and a decrease in the overall level of productivity, are determined.

Keywords: Lorenz model, mathematical modeling, model of economic development, optimal сontrol, deterministic chaos, climate changes.

full text

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UDC 517.9

MATHEMATICAL MODELING OF INSTABILITY IN ECOLOGICAL AND ECONOMIC SYSTEMS

REFERENCES

MATHEMATICAL MODELING OF INSTABILITY IN ECOLOGICAL
AND ECONOMIC SYSTEMS