Entropy model of dynamic chaos of an abiotic system

O.V. Bazarsky ^a*, Zh.Yu. Kochetovа ^{a **}, V.V. Kul’nev ^b***, D.A. Panteleev ^a****

^aZhukovsky and Gagarin Air Force Academy, Voronezh, 394004 Russia

^bCentral Chernozem Interregional Department of the Federal Service for Supervision
of Nature Management, Voronezh, 394087 Russia

E-mail: ^*arhangelskaya49@mail.ru,^**zk_vva@mail.ru,
^***kulneff.vadim@yandex.ru, ^****dmitryipanteleev@mail.ru

Received August 8, 2022; Accepted October 21, 2022

ORIGINAL ARTICLE

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DOI: 10.26907/2542-064X.2023.2.281-294

For citation: Bazarsky O.V., Kochetovа Zh.Yu., Kul’nev V.V., Panteleev D.A. Entropy model of dynamic chaos of an abiotic system. Uchenye Zapiski Kazanskogo Universiteta. Seriya Estestvennye Nauki, 2023, vol. 165, no. 2, pp. 281–294. doi: 10.26907/2542-064X.2023.2.281-294. (In Russian) 

Abstract

Dynamic chaos systems are commonly described by the nonlinear cyclic Verhulst relation. In this study, its use was extended to track the degradation of ecological systems at different stages of their development. A new concept was introduced: the geochemical entropy of abiotic ecological systems, which varies in the interval [0, 4] and determines the level of their stability in the interval [0, 1]. The model was verified by assessing soil pollution in Lipetsk (Russia). Despite the high level of soil pollution in certain areas of the city, the overall ecological situation turned out to be “normal” with a high level of stability (0.98). Forecasts were made of how the ecological situation in Lipetsk might develop with a change in the anthropogenic load. If it remains unchanged, the sustainability of the ecological system will be virtually the same. With heavier soil pollution, the stability may be lost at different rates, depending on the entropy of the system. The proposed model is helpful for assessing the current geo-ecological state of large territories with high anthropogenic load and pollution levels varying considerably between different areas of these territories, as well as for predicting the level of living comfort in urban agglomerations and managing ecological systems.

Keywords: Verhulst model, dynamic chaos, entropy, sustainability of the ecological system, forecast of the ecological situation, soil pollution, heavy metals

Figure Captions

Fig. 1. Diagram showing the development of a dynamic chaos system.

Fig. 2. Soil pollution map of Lipetsk.

Fig. 3. Histograms of the hazard quotients of major soil pollutants in Lipetsk.

Fig. 4. Forecast of the development of the ecological situation in Lipetsk for the next 30 years with different trends in the environmental policy.

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