The Dynamics of Modified Leslie-Gower Predator-Prey Model Under the Influence of Nonlinear Harvesting and Fear Effect

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.