Bifurcation and invariant manifolds of the logistic competition model

被引：22

作者：

Guzowska, Malgorzata ^{[2
]}

Luis, Rafael ^{[1
]}

Elaydi, Saber ^{[3
]}

机构：

[1] Univ Tecn Lisboa, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Lisbon, Portugal

[2] Univ Szczecin, Dept Econometr & Stat, Szczecin, Poland

[3] Trinity Univ, Dept Math, San Antonio, TX 78212 USA

来源：

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS | 2011年 / 17卷 / 12期

关键词：

stability; bifurcation; competition model; centre manifolds; unstable and stable manifolds; DISCRETE; EXCLUSION;

D O I：

10.1080/10236198.2010.504377

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important centre manifolds, and study their bifurcation. Saddle-node and period-doubling bifurcation route to chaos are exhibited via numerical simulations.

引用

页码：1851 / 1872

页数：22

共 21 条

[1]

[Anonymous], ADV DISCRETE DYNAMIC

[2]

[Anonymous], FRACTALS

[3]

[Anonymous], CTR MANIFOLDS NORMAL

[4] The parameterization method for invariant manifolds I:: Manifolds associated to non-resonant subspaces [J].

Cabré, X ;

Fontich, E ;

De la Llave, R .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2003, 52 (02) :283-328

[5]

Carr J., 1981, Applications of Center Manifold Theory, DOI [DOI 10.1007/978-1-4612-5929-9, 10.1007/978-1-4612-5929-9]

[6] Some discrete competition models and the competitive exclusion principle [J].

Cushing, JM ;

Levarge, S ;

Chitnis, N ;

Henson, SM .

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2004, 10 (13-15) :1139-1151

[7]

Elaydi S., 2008, DISCRETE CHAOS APPL

[8] MUTUAL EXCLUSION VERSUS COEXISTENCE FOR DISCRETE COMPETITIVE-SYSTEMS [J].

FRANKE, JE ;

YAKUBU, AA .

JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 30 (02) :161-168

[9] Global dynamics in macroeconomics: an overlapping generations example [J].

Gomis-Porqueras, P ;

Haro, A .

JOURNAL OF ECONOMIC DYNAMICS & CONTROL, 2003, 27 (11-12) :1941-1959

[10] DISCRETE-TIME MODELS FOR 2-SPECIES COMPETITION [J].

HASSELL, MP ;

COMINS, HN .

THEORETICAL POPULATION BIOLOGY, 1976, 9 (02) :202-221

← 1 2 3 →