Dynamical Analysis of Modified Leslie-Gower Beddington-DeAngelis Model with Prey Refuge and Intraspecific Competition

This study examines the dynamical behavior of a predator–prey model depicting the interaction between Perca fluviatilis (predator) and its natural prey, Rutilus rutilus. The model is formulated within a modified Leslie-Gower framework and employs the Beddington–DeAngelis functional response to capture mutual interference among predators during foraging. It further incorporates key ecological elements: prey refuge and nonlinear intraspecific competition arising from prey density dependence. Equilibrium points and their local stability are investigated using the Jacobian matrix and the Routh–Hurwitz criteria. The analysis identifies four equilibria: the trivial equilibrium, the predator-extinction equilibrium, the prey–extinction equilibrium, and the coexistence equilibrium. Numerical simulations corroborate these analytical results. The simulations reveal that under appropriate parameters, the stability of the system is significantly driven by both the availability of prey refuges and the degree of intraspecific competition, which ultimately determine the survival conditions for both populations.