Dynamic Response of Allee Effect and Refuge on the Interacting Species Model System

The present concern is to explore the complexity of the dynamics of a Leslie-Gower predator-prey model with the inclusion of the Allee effect and a constant proportion of prey refuge. Due attention is paid on the non-negativity, dissipativity, uniform boundedness and permanence of the dynamical system as well. Theoretical investigation is carried out on the existence of feasible equilibria of the system followed by the deductions imperative for the conditions of stability of the interior equilibrium. The analysis corresponding to the global stability of equilibrium using a suit-able Lyapunov function is, however, not ruled out from the present pursuit. Moreover, the analytical conditions for the occurrence of bifurcation phe-nomena are ascertained both for a saddle-node bifurcation and a Hopf bifur-cation. Numerical simulations are implemented finally at the end in order to validate the theoretical outcomes together with the concluding remarks relevant to the biological implications.(c) 2023 L&H Scientific Publishing, LLC. All rights reserved.