Differentical equations, dynamical systems and optimal control

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

Abstract: 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.

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

UDC: 519.6

MSC: 35Q92, 92D25

Received July 30, 2024, published October 21, 2024

Language: English

DOI: 10.33048/semi.2024.21.052