Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

Shengqiang Liu; Mahiéddine Kouche; Nasser Eddine Tatar

doi:10.1016/j.jmaa.2004.07.017

Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

Shengqiang Liu^*
, Mahiéddine Kouche
, Nasser Eddine Tatar

^*Corresponding author for this work

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

16 Scopus citations

Abstract

In this paper we consider a nonautonomous stage-structured competitive system of n-species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions. We obtain, by using the method of repeated replace, sufficient conditions for permanence and extinction of the species. The global attractivity of the unique positive equilibrium is proved in the autonomous case. Our results extend previous ones obtained by Liu et al. in [Nonlinear Anal. 51 (2002) 1347-1361; J. Math. Anal Appl. 274 (2002) 667-684].

Original language	English
Pages (from-to)	187-207
Number of pages	21
Journal	Journal of Mathematical Analysis and Applications
Volume	301
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.07.017
State	Published - 1 Jan 2005

Bibliographical note

Funding Information:
The first author is supported by Academy of Finland and the Chinese Postdoctoral Science Foundation. The third author thanks King Fahd University of Petroleum and Minerals for its financial support.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 15 Life on Land

Keywords

Distributed delays
Extinction
Global asymptotic stability
Interspecific competition
Permanence
Stage structure

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2004.07.017

Cite this

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title = "Permanence extinction and global asymptotic stability in a stage structured system with distributed delays",

abstract = "In this paper we consider a nonautonomous stage-structured competitive system of n-species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions. We obtain, by using the method of repeated replace, sufficient conditions for permanence and extinction of the species. The global attractivity of the unique positive equilibrium is proved in the autonomous case. Our results extend previous ones obtained by Liu et al. in [Nonlinear Anal. 51 (2002) 1347-1361; J. Math. Anal Appl. 274 (2002) 667-684].",

keywords = "Distributed delays, Extinction, Global asymptotic stability, Interspecific competition, Permanence, Stage structure",

author = "Shengqiang Liu and Mahi{\'e}ddine Kouche and Tatar, \{Nasser Eddine\}",

note = "Funding Information: The first author is supported by Academy of Finland and the Chinese Postdoctoral Science Foundation. The third author thanks King Fahd University of Petroleum and Minerals for its financial support.",

year = "2005",

month = jan,

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doi = "10.1016/j.jmaa.2004.07.017",

language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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T1 - Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

AU - Liu, Shengqiang

AU - Kouche, Mahiéddine

AU - Tatar, Nasser Eddine

N1 - Funding Information: The first author is supported by Academy of Finland and the Chinese Postdoctoral Science Foundation. The third author thanks King Fahd University of Petroleum and Minerals for its financial support.

PY - 2005/1/1

Y1 - 2005/1/1

N2 - In this paper we consider a nonautonomous stage-structured competitive system of n-species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions. We obtain, by using the method of repeated replace, sufficient conditions for permanence and extinction of the species. The global attractivity of the unique positive equilibrium is proved in the autonomous case. Our results extend previous ones obtained by Liu et al. in [Nonlinear Anal. 51 (2002) 1347-1361; J. Math. Anal Appl. 274 (2002) 667-684].

AB - In this paper we consider a nonautonomous stage-structured competitive system of n-species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions. We obtain, by using the method of repeated replace, sufficient conditions for permanence and extinction of the species. The global attractivity of the unique positive equilibrium is proved in the autonomous case. Our results extend previous ones obtained by Liu et al. in [Nonlinear Anal. 51 (2002) 1347-1361; J. Math. Anal Appl. 274 (2002) 667-684].

KW - Distributed delays

KW - Extinction

KW - Global asymptotic stability

KW - Interspecific competition

KW - Permanence

KW - Stage structure

UR - https://www.scopus.com/pages/publications/10144219961

U2 - 10.1016/j.jmaa.2004.07.017

DO - 10.1016/j.jmaa.2004.07.017

M3 - Article

AN - SCOPUS:10144219961

SN - 0022-247X

VL - 301

SP - 187

EP - 207

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

Abstract

Bibliographical note

UN SDGs

Keywords

ASJC Scopus subject areas

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