On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

Abstract

A three‐species food chain model with Allee and fear effects on both prey and predator is investigated in this work. The model consists of ODEs describing the evolution and interaction of prey, predator, and top predator populations in a biological system. We assume that the intrinsic growth rate of the prey is much smaller than a threshold value determined by other biological parameters of the model. Consequently, the model is transformed into a singularly perturbed system that acts on two different time scales, ranging from slow for both prey and predator to fast for the top predator. Positivity and boundedness of the solutions of the model along with the stability for its equilibria are investigated. The model possesses the exact invariant manifold with changing stability (black swan) and exhibits the canard phenomenon. Some numerical simulations are performed to validate our analysis.