Allee-induced Bubbling Phenomena in an Interacting Species Model

In this study, the Allee effect and hyperbolic saturated competence among predators are explored within a two-dimensional species interaction framework. The stability of the system’s feasible equilibria and different bifurcation patterns are examined using theoretical and numerical analyses. The local and global bifurcations of the proposed system are thoroughly analysed, employing one-parameter bifurcation diagrams with a chosen system parameter as the bifurcating factor. Additionally, a two-parameter bifurcation diagram is constructed to comprehensively evaluate the system’s dynamics, dividing the phase plane into distinct regions and capturing the system’s responses in each region. The model exhibits multi-stability phenomena, including bi-stability and tri-stability scenarios, indicating the presence of diverse attractors. Our research delves deeply into the Allee effect and saturated competence among predators, enhancing the quality of this investigation. Various numerical simulations are conducted to visually represent our analytical findings.