Persistence and Global Dynamics of an Extended Rosenzweig-MacArthur Model

Abstract

This paper investigates persistence and global dynamics of a tritrophic food chain model consisting of prey, predator, and super-predator. We establish dissipativeness, ultimate boundedness of an invariant region in the state space of this model via the notion of omega-limit sets, absorbing region and global attractor. We explore Freedman-Waltman theorem, and Bendixson-Dulac theorem to guarantee persistence conditions of the model. Lyapunov’s functionals and Lyapunov-LaSalle invariance principle ensure the existence of global asymptotic stability of the system. Numerical responses, phase-portrait and phase-flows were used to illustrate propositions and lemmas.

Key words: Global asymptotic stability; Lyapunov functional; Persistence.