Victor Ilyich Mikhailovsky

Summary Soil erosion as one of the types of land degradation aff ects various economic interests of people. It is shown that the most promising areas of erosion studies, where economic methods can be applied, are — assessment of actual damage fr om soil erosion, determination of the magnitude of probable damage from the occurrence of erosion
processes in soils, economic analysis in the development of sustainable land use systems for territories whose soils are subject to erosion. Th e group of methods for determining economic damage is characterized by the greatest development, including taking into account ecosystem services that soils «lose» as a result of erosion processes. Methods for assessing the risk of soil erosion have signifi cant development potential, since by now a powerful database of predictive models and equations (USLE, RUSLE, RUSLE2, WEPP, EUROSE, CREAMS, EPIC, VNIIZiZPE, etc.) has been created, allowing to assess indicators of soil erosion in the future. Th e neoclassical theory of capital is used in the development of sustainable land use systems, which requires that the fertility of the soil and the net social benefits from non-market goods and services from agricultural land should be maintained over time. Th us, it is possible to
create compensatory taxation mechanisms for territories wh ere soil erosion processes occur.

It is shown that time has always been considered by soil scientists as a “special” factor of soil formation — the form of the soil's existence as a material body. Soil formation processes are almost always nonlinear in time and cyclical (often this cyclicity is interrupted by the flow of soil formation). The soil, as a natural body, on the one hand, obeys the internal laws of self-development (in particular, the erasure of “lithological memory” and the development of “soil memory” during one stage /spurt of evolution), on the other hand, is subject to various (including anthropogenic) factors of influence, theoretically, all types of nonlinear dynamic behaviors - chaos, multistability, amplitude decay, solitons. The change in soil condition over time within one stage of their multi-stage evolution is usually described by a logistic equation. Differentiating the state function S from time t allows us to get an idea of the rate dS/dt and acceleration d2S/dt2 of soil formation processes. The inflection points on the soil condition graph become the extreme points on the graphs of derivatives of soil formation. It is noted that dissipative processes prevail in the “first half”, and antidissipative processes prevail in the “second half” of each stage of evolution. The predominance of dissipative processes over antidissipative ones is not homogeneous at all: at first it occurs at the start of the acceleration of soil formation, and then — at the stage of decrease.