Allee-induced periodicity and bifurcations in a Gause-type model with interference phenomena

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.