Complex Dynamical Behaviors of a Leslie-Gower Predator-Prey Model with Herd Behavior (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we consider a Leslie-Gower predator-prey modelwith a square root functional response while prey forms a herd as a form ofgroup defense. We show that the solution of the system is non-negative andbounded. By applying the blow-up technique, it can be deduced that theorigin displays instability. Moreover, employing the proof-by-contradictionapproach, we demonstrate that the unique equilibrium point can be globallyasymptotically stable under certain conditions. The sufficient conditions forthe occurrence, stability, and direction of Hopf bifurcation are obtained. Wefurther explore the conditions for the existence and uniqueness of the limitcycle. Theoretical results are validated through numerical simulations. Thus,our findings reveal that herd behavior has an important impact on the Leslie-Gower prey-predator system.