Mathematical Modeling

Tangential control of a predator-prey system with intraspecific predator competition

A. S. Ivanova^a, U. V. Krasnaya<sup>b

a</sup> Karelian Research Center Russian Academy of Science, Petrozavodsk, Russian Federation
^b Petrozavodsk State University, Petrozavodsk, Russian Federation

Abstract: A system of tree ordinary differential equations is researched. This system describes the dynamics of the numerical characteristics of predators and prey inhabiting a certain patch and the trophic attractiveness of the patch. It is assumed that the predator population will leave the patch if the food attractiveness falls to zero and there not enough prey for the predator population. The problem of preserving the species composition of the biocommunity of the patch is solved by removing some part of the predator population and moving it to another patch. The time intervals and the corresponding removal intensities that provide the solution to the problem have been found. The solution that is optimal in terms of minimizing the implementation costs was selected by numerical modeling from among the solutions constructed.

Keywords: system of three ordinary differential equations, intraspecific predator competition, trophic attractiveness of the patch, preserving the species composition of the biocommunity, tangential control.

UDC: 517.977

MSC: 34C99

Received: 02.06.2025

DOI: 10.14529/mmp250403