A detailed analysis of the spatial dynamics of a food-chain model with Allee and fear effect

We investigate the spatiotemporal dynamics of a tri-trophic food chain model incorporating a strong Allee effect on the prey and a fear effect on the middle predator. The model’s wellposedness is established through the positivity and boundedness of solutions. We derive all equilibria and examine their local stability, revealing saddle-node and transcritical bifurcations under varying parameter conditions. The analysis demonstrates how shifts in the Allee threshold and fear intensity induce bistability, coexistence, or extinction. Numerical simulations highlight diffusion-driven instabilities and complex Turing patterns, including labyrinthine formations and unexpected “leaser slime” structures—resembling those observed in fungi and algae in aquatic systems. These findings reveal the crucial role of behavioral and ecological feedbacks in shaping pattern formation and species persistence.