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

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