A Study of Stability and Bifurcation in a Discretized Predator–Prey Model With Holling Type III Response and Prey Refuge Via Piecewise Constant Argument Method

Abstract

This study explores the dynamics of a discrete-time predator–prey system, incorporating a Holling type III functional response and prey refuge, through the piecewise constant argument method. This method keeps things consistent and prevents negative population values, which is often a drawback of older techniques. We take a closer look at fixed points, exploring their existence and stability. We identify the conditions that lead to period-doubling and Neimark–Sacker bifurcations, and we back up our findings with numerical simulations. Our findings emphasize how important the predation coefficient is for keeping ecological balance and show that, in this model setup, the refuge for prey has a minimal effect on the stability of the system. These insights help us better understand the relationships between predators and their prey, providing valuable guidance for conserving biodiversity and managing ecosystems.