Diverse bifurcation structures and multi-stability in interacting species dynamics

This paper is propagated by introducing an interacting species system that incorporates the Allee effect and non-linear harvesting. The feasibility of the model is established through the discussion of essential preliminaries. The stability of the system around three alternative equilibria, namely, trivial, axial, and interior, is examined, along with various bifurcation structures. A thorough dynamic analysis of the proposed systems local and global bifurcations has been revealed through theoretical and numerical findings. The model system is comprehended by depicting one-parameter bifurcation diagrams, with a suitable system parameter selected as the bifurcating parameter. Moreover, to extensively study the system dynamics, a two-parameter bifurcation diagram has been portrayed, which divides the entire phase plane into several regions and records the systems responses in each region. The existence of several heterogeneous attractors has been detected as the model system exhibits multi-stability phenomena in the form of bi-stability and tri-stability situations. The impact of the Allee effect and non-linear harvesting has been systematically explored, followed by a comparative analysis to enrich this study.