Dynamical Analysis of a Leslie-Gower Type Harvesting Model incorporating Nonlinear Harvesting and Fear Effect

Resumen

In this study, we developed and analyzed a prey–predator model incorporating psychological
effects induced by predation risk. The predation process is modeled using a Holling type II
functional response, while the prey population is subject to nonlinear harvesting represented by
a Michaelis–Menten-type function. The model’s equilibrium dynamics were investigated through
both analytical techniques and numerical simulations using hypothetical parameter values. Our
findings reveal that increasing fear intensity and catchability, as well as decreasing prey reproduction
and conversion rates, destabilize the interior equilibrium, potentially driving the system toward
prey-free states. Under reduced fear intensity, the system exhibits sustained oscillations through
subcritical Hopf bifurcation. Moreover, the emergence of generalized Hopf and Bogdanov–Takens
bifurcations within certain parameter regimes highlights the rich and complex dynamics governed
by the interplay of ecological and behavioral factors.