Global stability for infinite-delay, dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches

Yang Kuang; Hal Smith; R. H. Martin

doi:10.1007/BF01049736

Global stability for infinite-delay, dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches

Yang Kuang, Hal Smith, R. H. Martin

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

20 Scopus citations

Abstract

A Lotka-Volterra-like model of m interacting species which can disperse among n discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when the n habitats are nearly identical.

Original language	English (US)
Pages (from-to)	339-360
Number of pages	22
Journal	Journal of Dynamics and Differential Equations
Volume	3
Issue number	3
DOIs	https://doi.org/10.1007/BF01049736
State	Published - Jul 1991

Keywords

AMS (MOS) subject classifications: Primary 34K30, Secondary 35R10, 34K15, 92A15
Global Stability
Razumikhin function
diffusive-delay Lotka-Volterra system
discrete patches
infinite delay

ASJC Scopus subject areas

Analysis

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10.1007/BF01049736

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abstract = "A Lotka-Volterra-like model of m interacting species which can disperse among n discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when the n habitats are nearly identical.",

keywords = "AMS (MOS) subject classifications: Primary 34K30, Secondary 35R10, 34K15, 92A15, Global Stability, Razumikhin function, diffusive-delay Lotka-Volterra system, discrete patches, infinite delay",

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year = "1991",

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T2 - Weakly interacting populations in nearly identical patches

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AU - Smith, Hal

AU - Martin, R. H.

PY - 1991/7

Y1 - 1991/7

N2 - A Lotka-Volterra-like model of m interacting species which can disperse among n discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when the n habitats are nearly identical.

AB - A Lotka-Volterra-like model of m interacting species which can disperse among n discrete habitats and where species interaction terms involve general unbounded delays is shown to possess a globally stable equilibrium when the undelayed intraspecific competition term dominates interspecific interactions as well as the delayed intraspecific competition effect and when the n habitats are nearly identical.

KW - AMS (MOS) subject classifications: Primary 34K30, Secondary 35R10, 34K15, 92A15

KW - Global Stability

KW - Razumikhin function

KW - diffusive-delay Lotka-Volterra system

KW - discrete patches

KW - infinite delay

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Global stability for infinite-delay, dispersive Lotka-Volterra systems: Weakly interacting populations in nearly identical patches

Abstract

Keywords

ASJC Scopus subject areas

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