The article describes a mathematical model which represents dynamics of the normalized difference vegetation index for winter wheat plantings in central black soil areas. As opposed to the approaches considered during our theoretical study, which, as a rule, are based on averaged data related to respectively vast territories (districts, regions, agricultural enterprises), this article describes a model which relates to rather small areas, namely to particular fields measuring 30-200 ha. The multiplicative model under consideration takes into account two opposite tendencies in the development of winter wheat: the process of phytomass increase and the process of plastic substances production. Parameters of the suggested model were estimated for winter wheat plantings in central black soil area on the fields with different levels of productivity for 2017 in accordance with normalized difference vegetation index data. We estimated the parameters by least square method. We performed model functional tests on the basis of the data received during remote sounding of the soil at more than one hundred of fields in Central Federal District. The test results are very promising. The suggested model allows for estimation of ripening period and the time of harvesting. The model can be applied for approximation of normalized difference vegetation index missing values, as well as for estimation of time required to attain maximum index value and, consequently, for forecasting of harvesting terms.
Numerical modeling of fractal sets using randomized iterated function systems can be implemented in two ways. The first of them is known as the chaos game, and the other is associated with the construction of a transformation matrix, the elements of which are the sums of terms of a converging series, divided by given classes. The last way allows us to relatively easily generate realizations of homeomorphic prefractal sets with similar topological properties.
The work is devoted to the analysis of cluster structures and enterprises in the agro-industrial sector of the Voronezh region from the point of system analysis view. In the framework of the systematic approach, the formed cluster structures have rank distributions corresponding to the hyperbolic Zipf's law. It is shown that the hyperbolic laws with a real indicator characterize formations with a systemic organization. The consideration of the formed cluster structures as system objects leads to the need to assess the shape of rank distributions. To verify the fulfillment of the systematic conditions of the analyzed agro-industrial cluster, the method of statistical tests was used. The article presents the results of testing on the data of the agro-industrial cluster in the Voronezh region, which allow coming to the conclusion about the nature of the ranking distribution. It is shown that the newly formed cluster of agricultural enterprises demonstrates the necessary properties of system formation. The fulfillment of the Zipf distribution on the constructed rank distribution confirms the assumption of the systemic nature of the new economic structure. In general, the results obtained indicate the perspectives of a new economic structure.
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