Qualitative Analysis of a Modified Leslie-Gower Model with Gestation Delay

This paper explores the qualitative analysis of a modified Leslie-Gower prey-predator model where the consumption rate of prey is by per capita predator according to Beddington-DeAngelis functional response. Moreover, time-lag (tau) is established to exploit a gestation period of predations. The permanence analysis of the proposed system is investigated. We study the local stability of the non-delayed model at all possible equilibrium points. It is demonstrated that the given model experiences Hopf bifurcation about the interior equilibrium point with respect to delay tau. Thereafter the stability and direction of Hopf bifurcation are formulated through normal and center manifold theorems. The derived criteria are justified with the help of numerical simulations. (C)2021 L&H Scientific Publishing, LLC. All rights reserved.