Multistability for a mathematical model of a tritrophic system in a heterogeneous habitat

Almasri A., Tsybulin V.G.
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We consider a spatiotemporal model of a tritrophic system describing the interaction between prey, predator, and superpredator in an environment with nonuniform resource distribution. The model incorporates superpredator omnivory (Intraguild Predation, IGP), diffusion, and directed migration (taxis), the latter modeled using a logarithmic function of resource availability and prey density. The primary focus is on analyzing the multistability of the system and the role of cosymmetry in the formation of continuous families of steady-state solutions. Using a numerical-analytical approach, we study both spatially homogeneous and inhomogeneous steady-state solutions. It is established that under additional relations between the parameters governing local predator interactions and diffusion coefficients, the system exhibits cosymmetry, leading to the emergence of a family of stable steady-state solutions proportional to the resource function. We demonstrate that the cosymmetry is independent of the resource function in the case of a heterogeneous environment. The stability of stationary distributions is investigated using spectral methods. Violation of the cosymmetry conditions results in the breakdown of the solution family and the emergence of isolated equilibria, as well as prolonged transient dynamics reflecting the system’s “memory” of the vanished states. Depending on initial conditions and parameters, the system exhibits transitions to single-predator regimes (survival of either the predator or superpredator) or predator coexistence. Numerical experiments based on the method of lines, which involves finite difference discretization in space and Runge –Kutta integration in time, confirm the system’s multistability and illustrate the disappearance of solution families when cosymmetry is broken.

Keywords: mathematical ecology, diffusion, taxis, cosymmetry theory, prey – predator – superpredator
Citation in English: Almasri A., Tsybulin V.G. Multistability for a mathematical model of a tritrophic system in a heterogeneous habitat // Computer Research and Modeling, 2025, vol. 17, no. 5, pp. 923-939
Citation in English: Almasri A., Tsybulin V.G. Multistability for a mathematical model of a tritrophic system in a heterogeneous habitat // Computer Research and Modeling, 2025, vol. 17, no. 5, pp. 923-939
DOI: 10.20537/2076-7633-2025-17-5-923-939
URL: http://crm-en.ics.org.ru/journal/article/3659/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Almasri A., Tsybulin V.G.

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