Dynamical analysis of a 3-species food chain model considering the impact of refuge and harvesting factors

This paper proposes a nonlinear mathematical model that describes the dynamics of a 3-species food chain consisting of a prey, an intermediate predator, and a top predator, while explicitly incorporating the effects of refuge and harvesting. Initially, the model’s fundamental qualitative properties, such as positivity, boundedness, and the existence and uniqueness of solutions, are examined. The existence of biologically feasible equilibrium points is derived, and their local stability is investigated using linearization and the Routh–Hurwitz stability criterion. Analytical conditions are obtained to ensure the stability of each equilibrium point. Furthermore, the global stability of the interior equilibrium point is examined by constructing an appropriate Lyapunov function. Numerical simulations are conducted to validate the analytical findings and to demonstrate the impact of key parameters on the system dynamics. Both analytical and numerical results indicate that, under suitable parameter conditions, the prey, intermediate predator, and top predator can coexist in a stable manner. The study highlights the significant role of refuge and harvesting mechanisms in maintaining long-term persistence of all species in the food chain.