Stability and bifurcation analysis of a discrete Leslie predator-prey model with fear effect

Abstract

This study examines a predator-prey model that includes the impact of fear and a square-root functional responseto represent herd behavior in the prey population. Our investigation aims to investigate the existence and stabilityof fixed points in this model. Through conducting an extensive analysis, we have uncovered valuable observations onthe model's behavior, namely recognizing the occurrence of period-doubling and Neimark-Sacker bifurcations.These findings provide an understanding of the intricate dynamics that govern predator-prey interactions in the presence of fear and herd behavior. We provide numerical examples to support our conclusions.