Tangential Control of a Predator-Prey System with Intraspecific Predator Competition

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

Keywords

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

References

1. Kirillov A.N., Ivanova A.S. Periodic and Quasiperiodic Control Processes in the Biocommunity Species Composition Preserving Problem. Transactions of the Karelian Research Centre of the Russian Academy of Sciences. Mathematical Modeling and Information Technologies Series, 2015, no. 10, pp. 99-106. DOI: 10.17076/mat148
2. Ivanova A.S., Kirillov A.N. Numerical Modeling of a Periodic Process that Preserves the Species Structure of a Biocommunity. Mathematical Models and Computer Simulations, 2022, vol. 14, no. 1, pp. 38-46. DOI: 10.1134/S2070048222010148
3. Kirillov A.N., Ivanova A.S. Method of Tangential Control of “Predator–Prey” System. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2025, vol. 18, no. 1, pp. 15–34. DOI: 10.14529/mmp250102
4. Andreeva E.A., Tsiruleva V.M., Kozheko L.G. The Model of Fisheries Management. Modeling, Optimization and Information Technology, 2017, no. 4 (19), 20 p.
5. Il’ichev V.G., Dashkevich L.V. Optimal Fishing and Evolution of Fish Migration Routes. Computer Research and Modeling, 2019, vol. 11, no. 5, pp. 879–893. DOI: 10.20537/2076-7633-2019-11-5-879-893
6. Kirillov A.N. Ecological Systems with Variable Dimension. OP and PM Surveys on Applied and Industrial Mathematics, 1999, vol. 6, no. 2, pp. 318–336. (in Russian)
7. Arditi R., Ginzburg L.R. Coupling in Predator-Prey Dynamics: Ratio-Dependence. Journal of Theoretical Biology, 1989, vol. 139, pp. 311–326. DOI: 10.1016/S0022-5193(89)80211-5
8. Hamilton W. Geometry for the Selfish Herd. Journal of the Theoretical Biology, 1971, vol. 31, no. 2, pp. 295–311. DOI: 10.1016/0022-5193(71)90189-5