Asymptotic behaviour of solutions of a Lotka-Volterra system

Nguyen Thi Hoai Linh, Ta Hong Quang, Ta Viet Ton

Published 2015-08-28Version 1

In this paper, we study a Lotka-Volterra model of two prey species and one predator species presented in \cite{SICE}. First, we give existence of an invariant set under a set of sufficient conditions of parameters in the model. These conditions also guarantee that the growth of all the species is permanent. Second, we present a condition under which the predator species falls into decay. Finally, by using Lyapunov functions, we prove global asymptotic stability of solutions of the model.