Limit cycles bifurcating of Kolmogorov systems in R2 and in R3

被引：8

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 50 条

[31] Modified mini finite element for the stokes problem in R2 or R3
Kim, Y
Lee, S
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2000, 12 (2-3) : 261 - 272
[32] FIVE LIMIT CYCLES TO A CLASS OF SYSTEMS IN R~3
Lianhua Ma
[J]. Annals of Applied Mathematics, 2011, (02) : 190 - 195
[33] THE REEB GRAPH OF A MAP GERM FROM R3 TO R2 WITH ISOLATED ZEROS
Batista, Erica Boizan
Ferreira Costa, Joao Carlos
Nuno-Ballesteros, Juan J.
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2017, 60 (02) : 319 - 348
[34] Analysis of a Cartesian PML approximation to acoustic scattering problems in R2 and R3
Bramble, James H.
Pasciak, Joseph E.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 247 : 209 - 230
[35] Countable Decompositions of R2 and R3 (vol 5, pg 325, 1990)
Komjath, Peter
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2024, 71 (03) : 1165 - 1165
[36] Tau R2 and R3 are essential regions for tau aggregation, seeding and propagation
Annadurai, Narendran
Malina, Lukas
Malohlava, Jakub
Hajduch, Marian
Das, Viswanath
[J]. BIOCHIMIE, 2022, 200 : 79 - 86
[37] SURGICAL TECHNIQUE OF EXTENDED LYMPHADENECTOMY (TYPE R2 AND R3) FOR GASTRIC ADENOCARCINOMAS
ELIAS, D
[J]. ANNALES DE CHIRURGIE, 1995, 49 (01): : 13 - 20
[38] On Modified Quaternionic Analysis, Gradient Dynamical Systems and Kolmogorov Equations in R3
Bryukhov, Dmitry
[J]. PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014), 2015, 1648
[39] SILYLATED DIPHOSPHITE COMPLEXES OF MOLYBDENUM - CRYSTAL-STRUCTURES OF THE COMPOUNDS MO(CO)4[P(OME)2O]2SIR2R3 (R2 = R3 = PH OR R2 = ME, R3 = PH)
SUM, V
KEE, TP
THORNTONPETT, M
[J]. JOURNAL OF ORGANOMETALLIC CHEMISTRY, 1992, 438 (1-2) : 89 - 98
[40] Kolmogorov's Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in R3
Chen, Gui-Qiang
Glimm, James
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 310 (01) : 267 - 283

← 1 2 3 4 5 →