A necessary and sufficient condition for global asymptotic stability of time-varying Lotka–Volterra predator–prey systems. (November 2015)

• Record Type: Journal Article
• Authors: Zheng, Wei; Sugie, Jitsuro
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 128
• Page End: 142
• Publication Date: 2015-11
• Subjects: 34C15 -- 34D05 -- 34D23 -- 37B25 -- 92D25; Global asymptotic stability -- Lotka–Volterra predator–prey model -- Weakly integrally positive -- Time-varying system; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.06.031
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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.