Кириллов А.Н., Сазонов А.М.
Модель «хищник–жертва» с переменной структурой взаимодействия
// Труды КарНЦ РАН. No 4. Сер. Математическое моделирование и информационные технологии. 2023. C. 36–40
Kirillov A.N., Sazonov A.M. Predator-prey model with a variable structure of interactions // Transactions of Karelian Research Centre of Russian Academy of Science. No 4. Mathematical Modeling and Information Technologies. 2023. P. 36–40
Keywords: dynamic systems; population dynamics; hybrid systems; sliding mode
The paper studies the problem of modeling the “predator-prey” population dynamics with intraspecific competition among the prey. The model has the form of a hybrid system (system with switching). The switching is between the interaction regime and the refugeregime, where the accessible prey numbers are so small that the predators cannot find the prey and there is no interaction between the populations. The sliding modes on the switching line were analyzed using the Filippov approach. The conditions for the existence of equilibrium and pseudo-equilibrium are derived, their global stability is proved.