Bifurcation analysis within a modified May-Holling-Tanner Prey-Predator system via Allee effect and harvesting on predator

In order to simulate predator expansion, this article integrates the Allee effect with simultaneous harvesting in an investigation of a Holling-Tanner predator-prey system. Under certain assumptions, our study indicates a maximum of three equilibrium points in the first quadrant. Additionally, we provide the prerequisites for populations of prey and predators to coexist. We also find parameter subsets in the system that lead to saddle-node and Hopf bifurcations. We derive the global stability criteria using Lyapunov functions. Our results are validated by numerical simulations performed using the MATCONT software in MATLAB. The model is more realistic now that an Allee effect and harvesting mechanisms have been added, representing the complexities of predator-prey dynamics in real-world ecosystems. The investigation of equilibrium points, bifurcation occurrences, and stability criteria contributes to the advancement of knowledge regarding the dynamics of ecological systems. This study emphasizes how important it is to take into account complex interactions when modeling ecosystems, especially when it comes to predator-prey dynamics. Subsequent studies might explore further ecological elements to enhance our comprehension of these systems. In conclusion, by clarifying important dynamics and offering insights into the behavior of predator-prey systems under various circumstances, our work advances ecological modeling.