Qualitative study of delayed predator--prey system in ecology

Abstract

On Earth, biological species like to form communities. Thus, studying this collective behavior in a predator-prey environment will provide more realistic findings. This article examines a predator-prey system in which both the prey and the predator exhibit swarm behavior. We begin by determining the linear stability of the system and then perform Hopf-bifurcation analysis on the consumption rate $(b)$. We then discussed the influence of time delay on the predation term since every biological function takes time to occur. We analyze the system's stability using a discrete-time delay, $\tau$ as a bifurcation parameter and perform Hopf-bifurcation analysis. Finally, numerical simulations are used to verify the analytical conclusions. This study will increase our knowledge of the dynamical behavior of realistic models in ecological systems.