In this paper, a stage-structured predator-prey system incorporating both fear effects and anti-predator behavior is investigated. Through rigorous mathematical analysis, the local and global stability of all equilibria is analyzed. The system exhibits complex bifurcation behaviors, including saddle-node, transcritical, Hopf, and Bogdanov-Takens bifurcations. Notably, anti-predator behavior plays a pivotal role in the system’s dynamics. As the intensity of anti-predator behavior increases, the system transitions from an unstable to a stable state. This dynamic shift indicates that weak anti-predator behavior facilitates the coexistence of prey and predator populations, accompanied by periodic oscillations. Conversely, strong anti-predator behavior leads to a stable state that drives the predator population toward extinction. Furthermore, a two-parameter bifurcation analysis, considering both anti-predator behavior and the fear effect, reveals bistability, highlighting the model’s rich dynamical structure. Our analysis reveals that while increased fear effect promotes system stabilization, it simultaneously drives predator population toward extinction-level thresholds. Meanwhile, a moderate rise in the maximum fear cost facilitates the long-term coexistence of both populations. This study is the first to simultaneously integrate the impact of the maximum cost of fear on prey mortality and the influence of anti-predator behavior on predator population density in a stage-structured predator-prey system. Our work extends existing stage-structured models and provides novel theoretical insights into the dynamic mechanisms underlying predator-prey interactions.
Meng et al. (Thu,) studied this question.