Dynamical Analysis of Discrete-Time Modified Leslie-Gower Predator-Prey with Fear Effect - Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus; Kusumawinahyu, Wuryansari Muharini (JTAM (Jurnal Teori dan Aplikasi Matematika), 2025)
It has been studied that fear plays a significant role in establishing ecological communities, influencing biodiversity, and preserving ecological balance in predator-prey interactions. In this study, it is proposed a discrete-time predator-prey model that takes the fear effect into account that is derived by using Euler method. Objective of this study is analyzing the model by linearization. Similar to the continuous model properties, the trivial fixed point and the predator-free fixed point are both unstable. The discrete model differs from the continuous model in that the stability of the interior fixed point and the free prey fixed point is affected by the time step size. Using numerical methods, we examine period-doubling bifurcations related to interior fixed point and prey-free point that are impacted by time step size.