Mathematical Investigation and Computers Simulation of Plant Protection Process Taking into Account the Temporary Age Structure and Arbitrary Tropic Functions

The problem of describing the process of protecting agricultural crops in mathematical modeling is relevant. Today, the problem of plant protection attracts the attention of a large circle of scientists in connection with its promising use in priority areas of development of science, technology and agriculture. Mathematical modeling of the process of protecting the planned crop is one of the main tools in predicting the state of natural systems and managing them. One of the most important national economic, social and environmental problems at present is the improvement of systems for protecting agricultural crops from pests. Mathematical modeling of the process of protecting the planned harvest obliges to improve regional systems for protecting cotton on the basis of a targeted ecological and biological study, revealing the specifics of the formation and development of agro ecosystems in intensive crop production. The main task of the integrated method of combating agricultural pests of the plant protection process is the management of agrocenoses of “harmful insects” and “beneficial insects” of species based on the use of biological, chemical methods as a means or a management tool.The use of mathematical methods and computer software products to solve the problem of protecting the planned crop significantly increases the efficiency of planned and economic work and ensure optimal results. In this paper, we consider a mathematical model of the plant protection process, taking into account the temporal age structure and arbitrary trophic functions, formulate the task of plant protection. Necessary and sufficient conditions for the solvability of the plant protection problem with arbitrary trophic functions are found.