Limit cycles bifurcating of Kolmogorov systems in R2 and in R3

被引：10

作者：

Llibre, Jaume ^{[1
]}

Paulina Martinez, Y. ^{[2
,3
]}

Valls, Claudia ^{[4
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Fac Ciencies, Barcelona 08193, Spain

[2] Ctr Recerca Matemat, Barcelona, Spain

[3] Univ Bio Bio, Fac Ciencias, Dept Matemat, Casilla 5-C, Concepcion, Chile

[4] Univ Lisbon, Ctr Math Anal Geometry & Dynam Syst, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2020年 / 91卷

基金：

欧盟地平线“2020”;

关键词：

Kolmogorov systems; Limit cycles; Hopf bifurcation; Zero-Hopf bifurcation;

D O I：

10.1016/j.cnsns.2020.105401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we consider the Kolmogorov system of degree 3 in R-2 and R-3 having an equilibrium point in the positive quadrant and octant, respectively. We provide sufficient conditions in order that the equilibrium point will be a Hopf point for the planar case and a zero-Hopf point for the spatial one. We study the limit cycles bifurcating from these equilibria using averaging theory of second and first order, respectively. We note that the equilibrium point is located in the quadrant or octant where the Kolmogorov systems have biological meaning. (c) 2020 Elsevier B.V. All rights reserved.

引用

页数：10

共 20 条

[1]

ans MM, 2020, COMMUN NONLINEAR SCI, V83, P18

[2]

Busse F.H, 1978, TRANSITION TURBULENC, VVolume 39

[3] Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model [J].

Du Chaoxiong ;

Wang Qinlong ;

Huang Wentao .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (03)

[4]

Guckenheimer J., 2002, APPL MATH SCI, V42

[5]

Guckenheimer J., 1980, LECT NOTES MATH, V898, P99, DOI DOI 10.1007/BFB0091910

[6]

Han M., 1998, J SYS SCI MATH SCI, V18, P403

[7] OSCILLATIONS IN LOTKA-VOLTERRA SYSTEMS OF CHEMICAL REACTIONS [J].

Hering, Roger H. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 1990, 5 (02) :197-202

[8]

Kolmogoroff A.N., 1936, Giornale Inst. Ital. Attuari, V7, P74

[9]

Kuznetsov YA, 2004, ELEMENTS APPL BIFURC, V2

[10]

Laval G., 1975, P SUMMER SCH THEORET

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