Дифференциальные уравнения, динамические системы и оптимальное управление

Multistability and dynamic scenarios in the prey–predator–superpredator model

Ahmad Almasri, V. G. Tsybulin

Southern Federal University, Milchakova St., 8-A, 344006, Rostov on Don, Russia

Аннотация: In mathematical models of population dynamics, the appearance of a continuum of solutions is a rare situation.  We analyze a multistability in the system of differential equations describing the prey-predator-superpredator dynamics. The cosymmetric approach is applied to derive a continuous family of equilibria for Beddington-DeAngelis functional response. The case of multistability was detected analytically and the destruction of the family of equilibria was studied. Our results exhibit memory of the disappeared family of equilibria and its impact on dynamic scenarios. Two-parameter bifurcation diagrams were built numerically for cosymmetric and general cases.

Ключевые слова: mathematical ecology, prey–predator–superpredator, differential equations, cosymmetry, multistability.

УДК: 519.6

MSC: 35Q92, 92D25

Поступила 30 июля 2024 г., опубликована 21 октября 2024 г.

Язык публикации: английский

DOI: 10.33048/semi.2024.21.052