Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays

Xu Rui; M. A. J. Chaplain; F. A. Davidson

doi:10.1080/00036810108840983

Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays

Xu Rui, M. A. J. Chaplain, F. A. Davidson

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.

Original language	English
Pages (from-to)	107-126
Number of pages	20
Journal	Applicable Analysis
Volume	80
Issue number	1-2
DOIs	https://doi.org/10.1080/00036810108840983
Publication status	Published - 2001

Keywords

Infinite delay
Global asymptotic stability
Lyapunov functional

Access to Document

10.1080/00036810108840983

Cite this

@article{546ac466f4584450833add50237c748d,

title = "Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays",

abstract = "In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.",

keywords = "Infinite delay, Global asymptotic stability, Lyapunov functional",

author = "Xu Rui and Chaplain, {M. A. J.} and Davidson, {F. A.}",

year = "2001",

doi = "10.1080/00036810108840983",

language = "English",

volume = "80",

pages = "107--126",

journal = "Applicable Analysis",

issn = "0003-6811",

publisher = "Taylor & Francis",

number = "1-2",

}

TY - JOUR

T1 - Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays

AU - Rui, Xu

AU - Chaplain, M. A. J.

AU - Davidson, F. A.

PY - 2001

Y1 - 2001

N2 - In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.

AB - In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.

KW - Infinite delay

KW - Global asymptotic stability

KW - Lyapunov functional

U2 - 10.1080/00036810108840983

DO - 10.1080/00036810108840983

M3 - Article

SN - 0003-6811

VL - 80

SP - 107

EP - 126

JO - Applicable Analysis

JF - Applicable Analysis

IS - 1-2

ER -

Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays

Abstract

Keywords

Access to Document

Fingerprint

Cite this