Mathematical model "consumer-resource" on a liner range and its application for modeling the spread of late blight of potato

Abstract

A model of consumer distribution on a fixed resource, which is uniformly distributed through a linear area, is presented. The model is based on the Cauchy problem for a system of partial differential equations. The stability of the system is studied. The physical basis of the model is the spread of late blight over the territory of a trophic resource. A qualitative picture of the process under consideration coincides with field data obtained as a result of modeling. The model describes "consumer" development not even at the moment, but through linear range. Thus assesment of damaged field square is possible.