Dynamic complexity of a discrete predator-prey model with prey refuge and herd behavior

Abstract

This paper examines a discrete predator-prey model's complex dynamics. Using bifurcation and center manifold theory, we study period-doubling and Neimark-Sacker bifurcations at positive fixed points and their direction. Numerical simulations confirm the theoretical conclusions that the model's dynamics rely on Euler method step size. The model's behavior is also affected by the prey population's conservation rate. The model suggests that excessive conservation may reduce predator populations, causing food shortages. Thus, predator-prey dynamics management must account for prey conservation rate