(untitled) (Nonlinear Studies, 2025)
This paper focuses on the inclusion of a refuge for prey and additional food for predator which introduces new dynamics and complexities to a stage-structured predator-prey model and analyzing the characteristic equations is a common approach to search for local stability of equilibria and identify the presence of Hopf-bifurcations in the model. Apart from this, a calculation of time delay and the investigation of Hopf-bifurcations around the interior equilibrium point have been conducted for various parametric values. These analyses provide valuable insights into the ecological influence of the model. The length of delay is estimated for which the stability continues to hold. Besides numerical simulation are carried out to authenticate our analytical findings. The biological implications of analytical as well as numerical findings are analyzed anxiously.