The Fear Effect in Prey-Predator Dynamics with Predator Intraspecific Competition

Abstract

Fear is an intrinsic factor in ecosystems and, contrary to common assumptions, exerts a measurable influence on prey-predator dynamics. This study analyses the impact of fear on the prey population in a Lotka-Volterra-type prey-predator system that incorporates intraspecific competition among predators. A system of ordinary differential equations is formulated, and stability and bifurcation analyses are then conducted. Numerical simulations and bifurcation continuation using AUTO, supported by symbolic computations in Maple and numerical integration in MATLAB, corroborate the theoretical results. Specifically, a one-parameter bifurcation with respect to the fear level reveals a transcritical bifurcation threshold that separates two regimes: below the threshold, a unique positive coexistence equilibrium is asymptotically stable, whereas above it, the interior state loses feasibility, and the dynamics converge to a predator-only equilibrium. Moreover, a two-parameter bifurcation analysis, by varying fear and predator competition, maps stability regions and shows that the bifurcation boundary shifts upward as competition strengthens, thereby enlarging the range of conditions that support coexistence. Numerical evidence further demonstrates that increasing fear consistently depresses prey abundance and may drive prey extinction, while predator density is regulated by competition. Overall, the study underscores the significant role of fear in shaping prey-predator dynamics and its potential to trigger qualitative shifts in ecosystem stability and population trajectories.