Predator Dynamics in a Fluctuating Environment: The Role of Allee Effects in a Bazykin-Type Model

This study develops a predator–prey model that incorporates logistic growth of the prey population, a Holling type II functional response, and both an Allee effect and intraspecific competition in the predator population. The nonlinear interactions between species are first examined using a deterministic framework. To better capture real ecological conditions, a stochastic component is then introduced to account for environmental variability and random fluctuations affecting population interactions. A comparative analysis of the deterministic and stochastic models is carried out to investigate the influence of ecological and environmental factors on population dynamics, with particular emphasis on stability, persistence, and extinction. Equilibrium points are analyzed to identify conditions that promote species coexistence or lead to population decline. The stochastic model further enhances understanding of predator–prey dynamics by revealing system vulnerability and resilience under environmental uncertainty. Numerical simulations are used to illustrate the theoretical results and to demonstrate the applicability of the model to real-world ecological systems. By integrating deterministic and stochastic perspectives, this study contributes to ecological modeling and provides insights relevant to ecosystem management and biodiversity conservation.