The influence of saturated fear effects on species dynamics: A Lotka–Volterra competition model analysis

Fear effects, as non-consumptive interactions in ecological systems, have emerged as a critical factor influencing species coexistence and population dynamics. Understanding the impact of fear effects on competing ecosystems helps humans better protect species and maintain ecological balance. In this paper, we propose and study a special Lotka–Volterra competition system, where one competitor experiences a reduction in birth rates and an increase in mortality rates due to fear of its competitor, and the effect of fear has saturated cost parameters [Formula: see text] and [Formula: see text]. The results show that using [Formula: see text] and [Formula: see text] as bifurcation parameters can induce transcritical and saddle-node bifurcations in the system. Furthermore, we find that the introduced saturated fear cost parameters [Formula: see text] and [Formula: see text] have interesting effects on the dynamical behavior of the Lotka–Volterra system. When the saturated fear cost parameters [Formula: see text] and [Formula: see text] satisfy certain conditions, the fear parameter [Formula: see text] does not affect the global stability of equilibria. Even under extreme fear, the two species are still able to coexist stably, which aligns with certain ecological phenomena. All theoretical results are verified through numerical simulations.