Darboux first integral conditions and integrability of the 3D Lotka-Volterra system

Authors
Cairo, L
Citation
L. Cairo, Darboux first integral conditions and integrability of the 3D Lotka-Volterra system, J NONL M PH, 7(4), 2000, pp. 511-531
Citations number
31
Categorie Soggetti
Physics
Journal title
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
ISSN journal
14029251 → ACNP
Volume
7
Issue
4
Year of publication
2000
Pages
511 - 531
Database
ISI
SICI code
1402-9251(200011)7:4<511:DFICAI>2.0.ZU;2-E
Abstract
We apply the Darboux theory of integrability to polynomial ODE's of dimensi on 3. Using this theory and computer algebra, we study the existence of rst integrals for the 3 dimensional Lotka-Volterra systems with polynomial inv ariant algebraic solutions linear and quadratic and determine numerous case s of integrability.