DARBOUX POLYNOMIALS FOR LOTKA-VOLTERRA SYSTEMS IN THREE DIMENSIONS

被引：17

作者：

Christodoulides, Yiannis T. ^{[1
]}

Damianou, Pantelis A. ^{[1
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2009年 / 16卷 / 03期

关键词：

Lotka-Volterra model; integrability; Darboux polynomials; HAMILTONIAN-SYSTEMS; 1ST INTEGRALS; DIFFERENTIAL-EQUATIONS; TODA LATTICE; INVARIANTS; INTEGRABILITY; FAMILIES;

D O I：

10.1142/S1402925109000261

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the parameters, and give the explicit form of the corresponding cofactors. More precisely, we show that a Darboux polynomial of degree greater than one is reducible. In fact, it is a product of linear Darboux polynomials and first integrals.

引用

页码：339 / 354

页数：16

共 50 条

[41] Local integrability and linearizability of three-dimensional Lotka-Volterra systems
Aziz, W. (waleed.aziz@plymouth.ac.uk), 2012, Elsevier Inc. (219)
[42] Computation of periodic orbits in three-dimensional Lotka-Volterra systems
Navarro, Juan F.
Poveda, Ruben
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (18) : 7185 - 7200
[43] Global stability for three-species Lotka-Volterra systems with delay
El-Owaidy, HM
Ismail, M
APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (2-3) : 301 - 306
[44] Local Integrability and Linearizability for Three Dimensional Lotka-Volterra Cubic Systems
Karim, Aween
Aziz, Waleed
Amen, Azad
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (01)
[45] Two limit cycles in three-dimensional Lotka-Volterra systems
Lu, ZY
Luo, Y
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 44 (1-2) : 51 - 66
[46] The positive definiteness of a class of polynomials from the global stability analysis of Lotka-Volterra systems
Lu, ZY
Wang, G
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1999, 38 (02) : 19 - 27
[47] Positive definiteness of a class of polynomials from the global stability analysis of Lotka-Volterra systems
Lu, Zhengyi
Wang, G.
Computers and Mathematics with Applications, 1999, 38 (02): : 19 - 27
[48] Impulsive control of multiple Lotka-Volterra systems
Dong, Lingzhen
Takeuchi, Yasuhiro
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (02) : 1144 - 1154
[49] ON THE INTEGRABILITY OF SOME GENERALIZED LOTKA-VOLTERRA SYSTEMS
BOUNTIS, TC
BIER, M
HIJMANS, J
PHYSICS LETTERS A, 1983, 97 (1-2) : 11 - 14
[50] Old and new results on Lotka-Volterra systems
Redheffer, Raymond
Nonlinear Analysis, Theory, Methods and Applications, 1997, 30 (06): : 3207 - 3213

← 1 2 3 4 5 →