Global stability of a predator–prey model with generalist predator

Abstract

Proof of the global stability for unique locally stable coexistence equilibrium points with the help of a suitable Lyapunov function is an interesting research problem for predator–prey type models. The proof of the global stability becomes challenging for the models which admit more than one coexistence equilibrium point. In this article, we prove the global stability of the coexistence equilibrium point for a predator–prey model with a generalist predator with the help of the Lyapunov function and the Bendixson–Dulac criteria under two different parametric restrictions. Further, we use a Lyapunov functional and apply LaSalle’s invariance principle to prove the global stability of the coexistence equilibrium point of the corresponding delayed model, with maturation delay.