Global Stability of Prey-Predator Model with Crowley-Martin type Functional Response and Stage Structure for Predator

Abstract

This article focuses on studying global stability of the prey-predator model with Crowley-Martin type functional response and stages structure for predator population. The analytical methods in this article are starting with the construction of a prey-predator model, determining stability of the equilibrium point by linearizing the model, analyzing the global stability of the equilibrium point using the Lyapunov method and the Krasovsky method, performing numerical simulations, and ecologically interpreting the global stability. The results of the study show that the prey-predator model with the Crowly-Martin type of functional response and stages structure of the predator population has one non-negative interior equilibrium point. The interior equilibrium point becomes globally asymptotically stable under a certain condition. This means that even if there is a tight interaction or predation on prey over a long period of time, the prey population will still be sustainable and also be stable. The global stability of the interior equilibrium gives an ecological interpretation that the ecosystem life is under control for a long period of time.