Predator–prey interactions: How prey refuge, additional food, seasonality, and stochasticity shape ecological stability?

In this study, we develop and analyze a deterministic prey–predator model where predators are generalist and follows modified Beverton–Holt-type growth dynamics due to additional foods, incorporating prey refuge. We also analyze system’s dynamics in the presence of seasonal and environmental fluctuations. Our key attention is on emphasizing the effects of density-dependent prey refuge and additional food availability on species coexistence and stability. Through theoretical analysis, we establish the feasibility of solutions under both autonomous and seasonal settings, identifying local stability criteria and the existence of positive periodic solutions. Our numerical results reveal that when there are no refuge and additional food, the system undergoes transcritical and supercritical Hopf bifurcations, leading to stable coexistence or population oscillations. However, the provision of prey refuge increases the number of coexistence equilibria, inducing bistability and, at higher levels, potential predator extinction. On variations of the levels of refuge and additional food, the system transitions from bistability to tristability, displaying complex dynamical shifts. However, the time variation of parameters significantly alter population stability, triggering periodic oscillations, chaotic regimes, and potential predator extinction under high-intensity of seasonal strengths. Sensitivity analysis confirms chaotic behavior under specific seasonal conditions, reinforcing the unpredictability of ecological dynamics. Notably, environmental noise can drive transitions between multiple equilibria, with moderate noise promoting coexistence and high noise leading to species extinction.