Global stability analysis of a ratio-dependent predator-prey system

A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymp- totic stability of the positive equilibrium. The...

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Bibliographic Details
Published inApplied mathematics and mechanics Vol. 29; no. 4; pp. 495 - 500
Main Author 鲁铁军 王美娟 刘妍
Format Journal Article
LanguageEnglish
Published Heidelberg Shanghai University Press 01.04.2008
College of Science,University of Shanghai for Science and Technology,Shanghai 200093,P.R.China
Subjects
Applications of Mathematics
Asymptotic properties
Classical Mechanics
Fluid- and Aerodynamics
Hopf bifurcation
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Stability
Stability analysis
功能反应
整体渐近线
比率相互性
稳定性
ratio-dependent
34D23
global asymptotic stability
functional response
O175.13
Hopf bifurcation
34C08
34D05
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ISSN0253-4827
1573-2754
DOI10.1007/s10483-008-0407-y

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Summary:A ratio dependent predator-prey system with Holling type Ⅲ functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymp- totic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.
Bibliography:O175.13
31-1650/O1
ratio-dependent, global asymptotic stability, functional response, Hopf bifurcation
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-008-0407-y