Abstract

Abstract: 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. Graphic abstract: (Figure presented.) © The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025.