Stability and bifurcation analysis of a complex two-prey, one-predator model with carry-over effects, migration, and harvesting

Predator-prey dynamics are crucial for shaping ecosystems. During foraging, prey must balance food intake with predator avoidance, often by using anti-predator behaviors to enhance their survival. Besides direct mortality caused by predators, indirect effects – such as the fear of predation and associated carry-over effects (COEs) – can significantly impact prey reproduction. Migration is common among many species, driven by the search for more favorable habitats, and some prey species employ group defense strategies to reduce their vulnerability to predators. This study introduces a three-species food-web model that incorporates fear-induced COEs, prey migration, and predator harvesting, consisting of two prey species and a single predator. The growth rate of one prey species is affected by predation-induced fear and its COEs, while the other prey species employs group defense strategies against the predator. We analyze the positivity, boundedness, and feasible equilibrium points of the model. We then examine the local stability and bifurcations of these equilibrium points. Finally, numerical simulations are used to investigate how parameters related to COEs and migration influence the system’s dynamics. The model exhibits diverse dynamical behaviors, including stable coexistence, periodic or multi-periodic oscillations, chaos, and species extinction.