Exploring the periodic behavior of a singular predator-prey system

In this paper, we delve into a singular periodic predator-prey system, a model that aptly captures the intricate dynamics of human population evolution on Easter Island. Based on the coincidence degree theory for first-order high-dimensional differential systems, we derive a novel result regarding the existence of positive periodic solution for this system. Additionally, we offer numerical simulations to visualize and substantiate our theoretical result.