Application of the logistic function in the modeling of erosion-slope catenae and bioproductivity of agrogeosystems

The relevance of this study is related to the need to summarize the material in various fields of research and translate this data into the language of digital models. Understanding the physical essence of the process is of great importance for mathematical modeling of slope ecogeomorphosystems and biological productivity of agrogeosystems the fundamental nature of the diffusion equation underlying these processes. The log function (LF) was chosen for the analytical description of processes, since it satisfies the representations occurring in the catenary complex at different taxonomic levels: micro-, meso-, macro- and mega-organizational landscapes. With the help of LF, the first and subsequent derivatives are relatively easy to calculate, which give ideas about the speed and acceleration of processes.

Materials and methods. The studies were conducted from 1986 to 2022.

Objects of research at the south-eastern end of the Volga upland: land use "Kachalinskoe" of the Federal Research Center of Agroecology of the Russian Academy of Sciences, land use of the Federal State Budgetary Institution VNIIOZ and on the lands of the Zavolzhskaya irrigation system (Volgograd region), as well as rainfed lands in the Mikhailovsky district of the "Ishkin" A.V. The study and modeling of the catenary complex log function was carried out at macro-, meso-levels.

Results and conclusions. As a result of studies of the features of the spatial distribution of transitional natural zones, a "Method for mapping natural transition zones (ecotones)" was developed and patented. The essence of the patent is the spatial analysis of transition zones in subboreal landscapes by radiation heat flow. The log function described the relationship of y(x) bioproductivity with soil washout (in normalized values) with parameters a=3.478; b=5.948; x=0.00001 – 1.0.The dependence is performed for chestnut soils of light, medium and heavy granulometric composition. The calculation based on the given dependence was performed by finding the first and subsequent derivatives. The logistic function with a high degree of approximation describes the morphometric changes that occur with agricultural crops during the growing season. These include the growth function of agricultural crops; sunflower (variety "Dainty" and hybrid LG-5456), barley ("Medicum 139"), varieties and hybrids of corn.

Conclusion. LF is universal.With the help of it, it is possible not only to analyze existing events, to predict the development of processes occurring on slope ecogeomorphosystems and in agrocenoses with sufficiently high accuracy.

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