https://doi.org/10.1140/epjb/s10051-025-00911-8
Regular Article - Statistical and Nonlinear Physics
Allee-induced periodicity and bifurcations in a Gause-type model with interference phenomena
1
Department of Mathematics, Visva-Bharati, 731235, Santiniketan, India
2
Departamento de Matematica, Fisica y Estadistica, Facultad de Ciencias Basicas, Universidad Catolica del Maule, Talca, Chile
3
Pontificia Universidad Catolica de Valparaiso, Valparaiso, Chile
Received:
29
December
2024
Accepted:
25
March
2025
Published online:
16
April
2025
Predator–prey models currently serve as essential tools in the mathematical modelling of ecological systems, given their broad applicability in understanding complex interactions. This study examines the dynamics of a Gause-type predation model, incorporating assumptions that specialist predators compete for resources and that the prey population experiences an Allee effect. The model exhibits diverse dynamical behaviours through this ecological framework, including bi-stability, revealing the system’s intricate structure. The analysis highlights the existence of codimension one and codimension two bifurcations involving positive equilibria, such as saddle-node, Hopf, Bogdanov–Takens and Bautin bifurcations. The multifaceted dynamics of the system are further analysed across bi-parametric regions, represented through a variety of phase portraits. The ecological implications of these findings are discussed in detail to offer insights into the dynamic behaviours observed. Numerical simulations are also conducted to verify the analytical results, illustrating the model’s robustness and applicability.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
