Dynamics of a family of Lotka-Volterra systems in R3

被引：7

作者：

Llibre, Jaume ^{[1
]}

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

机构：

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

[2] Ctr Recerca Matemat, Barcelona 08193, Catalonia, Spain

[3] Univ Bio Bio, Fac Ciencias, Dept Matemat, Concepcion, Chile

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 199卷

基金：

欧盟地平线“2020”;

关键词：

Lotka-Volterra; Integrability; Phase portraits; Poincare disc; DIFFERENTIAL-EQUATIONS; CLASSIFICATION;

D O I：

10.1016/j.na.2020.111915

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide the phase portraits of the 3-dimensional Lotka-Volterra systems (x) over dot = x(y + az), (y) over dot = y(x + z), (z) over dot = bz(- ax + y), for all the values of the parameters a and b, in the finite region and in the infinity region through the Poincare compactification. We also study the integrability of the system. (c) 2020 Elsevier Ltd. All rights reserved.

引用

页数：15

共 27 条

[1] On the global flow of a 3-dimensional Lotka-Volterra system [J].

Alavez-Ramirez, Justino ;

Ble, Gamaliel ;

Castellanos, Victor ;

Llibre, Jaume .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (10) :4114-4125

[2]

[Anonymous], 1973, Stability and Complexity in Model Ecosystems

[3]

Bautin NN., 1954, Prikl. Mat. Mech, V18, P128

[4] Integrability and global dynamics of the May-Leonard model [J].

Ble, Gamaliel ;

Castellanos, Victor ;

Llibre, Jaume ;

Quilantan, Ingrid .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (01) :280-293

[5] UNIVERSAL CANONICAL-FORMS FOR TIME-CONTINUOUS DYNAMICAL-SYSTEMS [J].

BRENIG, L ;

GORIELY, A .

PHYSICAL REVIEW A, 1989, 40 (07) :4119-4122

[6] COMPLETE FACTORIZATION AND ANALYTIC SOLUTIONS OF GENERALIZED LOTKA-VOLTERRA EQUATIONS [J].

BRENIG, L .

PHYSICS LETTERS A, 1988, 133 (7-8) :378-382

[7]

Busse F. H., 1981, Chaos and order in nature, V11, P36, DOI 10.1007/978-3-642-68304-6_4

[8] ALGEBRAIC AND TOPOLOGICAL CLASSIFICATION OF THE HOMOGENEOUS CUBIC VECTOR-FIELDS IN THE PLANE [J].

CIMA, A ;

LLIBRE, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1990, 147 (02) :420-448

[9]

Dumortier F, 2006, UNIVERSITEXT, P1

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

Hering, Roger H. .

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

← 1 2 3 →