Asymptotic behaviour and bifurcation in competitive Lotka-Volterra Systems

被引：3

作者：

Hou, Zhanyuan ^{[1
]}

机构：

[1] London Metropolitan Univ, Fac Comp, London N7 8DB, England

来源：

APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 02期

关键词：

Lotka-Volterra; Competitive systems; Bifurcation; Asymptotic behaviour; Global attraction; GLOBAL ATTRACTOR;

D O I：

10.1016/j.aml.2011.08.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A conjecture about global attraction in autonomous competitive Lotka-Volterra systems is clarified by investigating a special system with a circular matrix. Under suitable assumptions, this system meets the condition of the conjecture but Hopf bifurcation occurs in a particular instance. This shows that the conjecture is not true in general and the condition of the conjecture is too weak to guarantee global attraction of an equilibrium. Sufficient conditions for global attraction are also obtained for this system. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：195 / 199

页数：5

共 8 条

[1] Average growth and total permanence in a competitive Lotka-Volterra System [J].

Ahmad, Shair ;

Lazer, Alan C. .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2006, 185 (Suppl 5) :S47-S67

[2] TIME DELAYS IN N-SPECIES COMPETITION .1. GLOBAL STABILITY IN CONSTANT ENVIRONMENTS [J].

GOPALSAMY, K ;

AHLIP, RA .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1983, 27 (03) :427-441

[3]

Gopalsamy K., 2013, STABILITY OSCILLATIO, V74

[4]

Hassard B.D., 1981, Theory and Applications of Hopf Bifurcation

[5] Global attractor in competitive Lotka-Volterra systems [J].

Hou, Zhanyuan .

MATHEMATISCHE NACHRICHTEN, 2009, 282 (07) :995-1008

[6] Global attractor in autonomous competitive Lotka-Volterra systems [J].

Hou, ZY .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (12) :3633-3642

[7] POSITIVE SOLUTIONS OF POSITIVE LINEAR-SYSTEMS [J].

KAYKOBAD, M .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1985, 64 (JAN) :133-140

[8] Kolmogorov vector fields with robustly permanent subsystems [J].

Mierczynski, J ;

Schreiber, SJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 267 (01) :329-337

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