Abstract
Purpose. Purpose of this work is to analyze the mathematical model of slopes ecosystem on stability while distrib- uting the components of ecosystem pollutant with use of the compartment models method. To solve this task the following goals were set: to build the model of representative slopes ecosystem; to determine main characteristics of this ecosystem in purpose of assessment the distribution coefficient for this radionuclide; to create the mathematical description of migration with ecosystem compartments; to test the stability of mathematical model in setting of initial conditions disturbance; to analyze the results and make the relevant decisions. Methods. In this work the method of compartment models was used, which currently is being in active development stage in field of radiation biology. It consists in divid- ing the whole chain of radionuclides transfer into compartments (units). Interaction between the compartments is set up with radionuclide distribution and transfer coefficients. These coefficients define what fold is the activity of certain radionuclide can be higher (or lower) in the ecosystem components versus environment. Results. The conducted study showed that the mathematical model matrix describing radionuclide transfer is not degenerated, and this suggests the unity of stationary system decoupling. Matrix eigenvalues are negative. It means that system decoupling is stable against the initial conditions disturbance. It was calculated that stability reserve equals 0.35. Originality. Along with the conventional methods used in ecology, this method plays important role and allows determine quantitative and qualitative measurements of environment as well as it makes possible to predict the course of some chemical or physical-chemical pro- cesses with consideration of various parameters of certain impact. Practical value. Mathematical modeling of ecological processes is necessary to facilitate search of optimal operation mode for the natural and technological systems, to di- minish risks of harmful changes in ecosystem performance, to develop and implement some countermeasures for eco- systems improvement. Conclusions. This model can serve as a multipurpose tool while ecological processes modeling not only in pollution but also with other radionuclides or heavy metals.
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