A mathematical model of the problem of plant protection in a biosystem of the type “harmful insects–beneficial insects” with arbitrary trophic functions

When studying the agrocenosis of cotton, the problem arises of a formal description of its structures, i. e., a set of blocks in which the stocks of elements and energy are concentrated, and the flows connecting them within the agrocenosis, carrying out the transfer of matter and energy from the block to the block and, also, studies of stability issues — agrocenosis. The basis of cotton agrocenosis is the crop itself: cotton as a primary product. Due to cotton, a variety of organisms live — phytophages, cotton pests. Pests of cotton include aphids (black alfalfa, melon, and large cotton), scoops (cotton, small ground, and azimic), and spider mite. Pests find in cotton a copious source of food and multiply intensely. The author considers the mathematical problems of point models, i. e., when the population size depends on time. The so-called preparatory task of plant protection is formulated. Necessary and sufficient conditions for the solvability of preparatory problems of plant protection with arbitrary trophic functions are found.