The impact of alternative resources and fear on the dynamics of the food chain

In this paper, a three-species food chain model is proposed and studied. It is assumed that there are fear costs in the first two-level due to predation risk and there exists an alternative source of food for a top predator. Holling’s disc function is adopted to describe the food transition throughout the chain. All the solution properties are discussed. The conditions of local stability and persistence of the model are established. The Lyapunov function is used to specify the basin of attraction for each equilibrium. Local bifurcation analyses are studied. The global dynamics of the model are investigated numerically. Different bifurcation diagrams and attractors are obtained. It is obtained that the system is rich in dynamics that include chaos.