Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

Abstract

This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with MichaelisMenten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac's criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting.

Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish

“…The harvesting of a species is another key issue that arises within a prey-predator system. Harvesting is the process of catching, taking, or removing (animals), especially for food [51,52]. It is vital for social management and the protection of resources, both from an economic and ecological point of view [14,53].…”