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

Abstract

This article studies a discrete-time Leslie-Gower two predator-one prey system with Michaelis-Menten type prey harvesting. Positivity and boundedness of the model solution are investigated. Existence and stability of fixed points are examined. Using an iteration scheme and the comparison principle of difference equations, we find out the sufficient condition for global stability of the positive fixed point. It is shown that the sufficient criterion for Neimark-Sacker bifurcation can be developed. It is observed that the system behaves in a chaotic manner when a specific set of system parameters is chosen, which are regulated by a hybrid control method. Examples are provided to illustrate our conclusions.

Stage structured prey-predator model incorporating mortal peril consequential to inefficiency and habitat complexity in juvenile hunting

“…In cases where there are populations with overlapping generations, the birth processes take place in a continuous manner. As a result, the interaction between predator and prey is typically represented through the use of ordinary differential equations [29]. However, it is worth noting that in reality, there are other types of species, such as monocarpic plants and semelparous animals [30], that exhibit discrete non-overlapping generations and their births occurexclusively during regular breeding seasons.…”