Michaelis-Menten-Type Prey Harvesting in Discrete Modified Leslie-Gower Predator-Prey Model

Abstract

A discrete-time Michaelis-Menten-type prey harvesting is discussed in this paper, in the modified Leslie-Gower predator-prey model. Detailed analysis of the topology of nonnegative interior fixed points is given, including their existence and stability dynamics. Also, the conditions for the existence of flip and Neimark-Sacker bifurcations are derived by using the center manifold theorem and bifurcation theory. The numerical simulations are provided, using a computer package, to illustrate the consistency of theoretical results.

A Discrete-Time Modified Leslie-Gower Model with Double Allee Effect and Its Stability and Bifurcation Analysis

“…The relationships between different species on Earth can be modeled as predator-prey interactions, which are fundamental to the survival of many organisms [1,2]. Mathematical models can be used to approximate these dynamics.…”

“…However, the model possesses much richer dynamics A Discrete-Time Modified Leslie-Gower Model with Double Allee Effect 119 than previously established. This can be accomplished by examining the discrete version of system (1). Discretization is useful for ecosystems in which consecutive generations do not overlap.…”

“…Discretization is useful for ecosystems in which consecutive generations do not overlap. We utilize the forward Euler method to discretize system (1). The discrete version of system (1) with a step-size of h is defined as follows:…”

Global Stability and Bifurcation Analysis in a Discrete-Time Two Predator-One Prey Model with Michaelis-Menten Type Prey Harvesting

“…Ajaz et al [22] investigated the dynamical behaviour of a modified Leslie-Gower prey-predator model with harvesting in prey population and showed the existence and directions of period doubling and Neimark-Sacker at positive fixed point and also indicated chaos control when chaos emerge through bifurcation. Khan et al [23] discussed a discrete-time Michaelis-Menten type prey harvesting in the modified Leslie-Gower predator-prey model and obtained the conditions for the existence of flip and Neimark-Sacker bifurcations. Chen et al [24] studied a discrete Leslie-Gower predator-prey model with Michaelis-Menten prey harvesting and observed that the system can exhibit fold, flip and Neimark-Sacker bifurcations by the application of center manifold theorem and bifurcation theory.…”