Mathematical Analysis of a Predator–Prey Model Incorporating Prey Fear

This study analyzes a predator-prey ecosystem in which the prey serves as the predator’s preferred food source. The growth of the prey population is limited by two main factors: the availability of environmental resources and the fear induced by the presence of the predator. On the other hand, the predator population growth is constrained by the availability of both prey and an alternative food source. It is assumed that the time spent by predators on pursuing, subduing, consuming, and digesting prey—along with the time required to prepare for the next hunt—depends on the number of individuals in both populations. The work consists of a thorough qualitative analysis of the solutions to the system of equations associated with the proposed model. These analytical results are then validated through numerical simulations implemented in Python. Furthermore, a comparative study is carried out against a similar model that does not incorporate the prey’s fear response to the predator.