Exploring the Dynamics of Two Prey and One Predator System with Fear Effect - Nithya Dakshnamoorthy; Buddana Murty; Madhusudanan Vasudevan; Dadi Saraswathi (Jambura Journal of Biomathematics (JJBM), 2026)
This research focuses on analyzing a predator–prey system consisting of two prey species and one predator, where the prey experience fear due to the predator’s presence. The predator interacts with Prey I through a Holling Type I response and with Prey II through a Holling Type II response. Predators play a multifaceted role in shaping prey populations, as supported by biological research, by combining direct predation with indirect effects such as fear-induced stress and increased intraspecific competition. We analyzed the positivity, boundedness and condition for persistence of the system and investigate the presence of positive equilibrium points as well as their practicality. The Routh – Hurwitz condition is used to determine the stability locally at all equilibrium points. We show that the model's stability globally exists. Numerical simulations are performed to examine the system dynamics and the sensitivity to key parameters, including the fear response intensity and conversion coefficient. The results indicate that higher parameter values tend to produce oscillatory behavior, whereas lower carry-over effects promote system stability. Furthermore, the interaction between competition among Prey I and Prey II and predator-induced fear leads to a reduction in the long-term population sizes of both species. As the level of fear increases beyond a threshold, the system shifts from persistent oscillations to a stable equilibrium.