A necessary and sufficient condition for global asymptotic stability of time-varying Lotka-Volterra predator-prey systems

摘要

The purpose of this paper is to present a necessary and sufficient condition which guarantees that an interior equilibrium of a certain predator prey system is globally asymptotically stable. This ecological system is a model of Lotka Volterra type whose prey population receives time-variation of the environment. We assume that the time-varying coefficient is weakly integrally positive and has a weaker property than uniformly continuous. Our necessary and sufficient condition is expressed by an improper double integral on the time-varying coefficient. Our work is inspired by the study of the stability theory for damped linear oscillators. (C) 2015 Elsevier Ltd. All rights reserved.