Dynamical Analysis of Delayed Predator-Prey Models and Explicit Impacts of Harvesting

In theoretical ecology, mathematical models are formulated to understand the interaction among species in an ecosystem. This paper explores the dynamics of three predator -prey models with delay in prey -specific growth rate, predator response function, and predator interaction time respectively. Subsequently, the impact of harvesting is analyzed in all the models. It is observed that varying delay could instigate instability in the system via Hopf-bifurcation. Taking harvesting as control can destroy such oscillatory behavior and bring the system to a stable dynamic. In this interplay between these two parameters, stability switching is observed, and such results could not be ascertained in the latter models. We have also inspected the system's behavior at maximum sustainable yield (MSY). If delay is small, harvesting at MSY could produce stable stock. Various numerical simulations are carried out to visualize our analytical findings. (c) 2024 L&H Scientific Publishing, LLC. All rights reserved.