Dynamical analysis of time delay effects on the stability of a harvested predator-prey system with a general Holling type response

The study of predator-prey dynamics has long served as a cornerstone in ecological modelling. This research investigates a generalized predator-prey model incorporating a general Holling-type functional response, combined harvesting, and discrete time delays. The model considers both prey and predator harvesting strategies under realistic ecological constraints, and includes maturation and response delays to better capture biological interactions. Using qualitative analysis techniques, such as local stability, Hopf bifurcation, and numerical simulations, we explore the system's dynamic behavior. The goal of this research is to determine the optimal harvesting rate (or effort) that balances resource extraction with the need to maintain ecosystem stability and the long-term viability of both predator and prey populations. Findings from this study may inform sustainable harvesting policies and contribute to more accurate ecological forecasting models.