Dynamic analysis of a modified Leslie-Gower model with nonlinear prey harvesting and prey herd behavior

Abstract

In this study, a modified Leslie-Gower model with square root functional response has been used to describe prey group defense mechanism and nonlinear predator harvesting. Two equilibrium points are always present and feasible, whereas the predator-free equilibrium point and the interior equilibrium point are only present and feasible under a parametric condition. The equilibria’s local stability has been investigated. The saddle-node bifurcation at the axial equilibrium point is investigated using the harvesting coefficient as the bifurcation parameter. The maximum sustainable yield has been established discovering that if the value of harvesting rate is lower than the maximum sustainable yield, both populations will cohabit and the ecological balance will be maintained. By establishing harvesting rate control parameters with the goal of achieving sustainable development of people and ecosystems as the starting point, an optimal control model of harvesting rate mechanisms. Fisheries management will be aware of the rate at which little fish species (preys) must be taken in order to maintain ecological balance based on the findings of this study. Additional numerical simulations are run to validate the findings.