Abstract
A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is developed and investigated in this study. The predator is supposed to feed on the prey using Holling type-II functional response. The goal is to see how fear of predation and presence of harvesting affect the model's dynamics. The system's positivity and boundlessness are demonstrated. All conceivable equilibria's existence and stability requirements are established. All sorts of local bifurcation occurrence conditions are presented. Extensive numerical simulations of the proposed model are shown in form of Phase portraits and direction fields. That is to guarantee the correctness of the theoretical results of the dynamic behavior of the system and to confirm the existence of various forms of bifurcations. The fear rate is observed to have a stabilizing effect up to a threshold value, after which it leads to prey extinction. The harvesting coefficients, on the other hand, serve as control parameters that, when exceeded, trigger the system to extinction.
Highlights
One of the most popular subjects in biomathematics is population dynamics
The effect of changing the parameters on the model's dynamics is investigated by looking at the possibilities of local bifurcation types such as saddle-node, transcritical, and pitchfork bifurcation
The system has two unstable interior equilibrium points with three axial equilibrium points and a saddlenode trivial equilibrium point for data set #2. This ensures that the system's dynamics are rich, and the number of equilibrium points is determined by the data parameters
Summary
One of the most popular subjects in biomathematics is population dynamics. The study of the evolution of diverse populations has always been of special interest, beginning with populations of a single species and progressing to more realistic models in which several species exist and interact in the same ecosystem. Predators can devour other populations when food is scarce, but their growth will be limited since their primary prey is scarce To consider this issue, Aziz-Alaoui and Okiye [20] suggested a modified Leslie–Gower model by introducing a constant b in the denominator of Leslie-Gower term that measures environmental protection for the predator to avoid singularities when x = 0. Many experts began to study the predator-prey model with fear effect; see [3, 6] The dynamics and bifurcations of a modified Leslie-Gower predator-prey model with HollingII functional response and nonlinear harvesting in both the prey and predator communities are investigated in this paper, as well as the influence of the fear factor. Since the right-hand side of the interaction functions of the system (5) are continuous and have continuous partial derivatives, system (5) has a unique solution that belongs to the positive quadrant R
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