Predator–Prey Dynamical Behavior and Stability Analysis with Square Root Functional Response

Abstract

One of the main characteristics of the ecological systems is the relationship between species and their living environment. For that reason modeling of predator–prey interactions are one of the important factors in mathematical biology. For the classical predator–prey models, the crucial components are the growth function of prey species in the absence of a predator, the mortality function of predator species in the absence of prey and the functional response function of the predator to the prey. In this paper, we consider a different predator–prey model in which the prey exhibits herd behavior so that the predator interacts with the prey along the outer corridor of the herd of the prey. The purpose of the work is to study the local stability, global stability and limit cycle of our proposed model. Some numerical simulations are carried out to support our analytical findings.