The Significance of Cannibalism, Panic, and Sanctuary in the Interactions Between Prey and Predator with a Stage Structure

This paper analyzes a novel prey-predator model that takes into account the predator's stage structure, cannibalism within the predator population, panicky behavior, and the existence of a sanctuary where the prey might hide from the predator. The Holling type II functional response is used in the predation process. The behavior of the identified fixed points of the proposed system has been closely analyzed. The analysis focuses on the local stability and potential bifurcations that could happen close to the system's fixed points. The Lyapunov function approach is used to investigate the fixed-point stability zone globally. Numerical simulations were run to confirm the analytical findings as well as to test the model's long-term behavior to understand the impact of changing the system's parameters. It is noted that the system exhibits a variety of local bifurcations, most notably the Hopf bifurcation, which is calculated numerically for various parameters.