Darboux method and search of invariants for the Lotka-Volterra and complexquadratic systems

Authors
Cairo, L Feix, MR Llibre, J
Citation
L. Cairo et al., Darboux method and search of invariants for the Lotka-Volterra and complexquadratic systems, J MATH PHYS, 40(4), 1999, pp. 2074-2091
Citations number
12
Categorie Soggetti
Physics
Journal title
JOURNAL OF MATHEMATICAL PHYSICS
ISSN journal
00222488 → ACNP
Volume
40
Issue
4
Year of publication
1999
Pages
2074 - 2091
Database
ISI
SICI code
0022-2488(199904)40:4<2074:DMASOI>2.0.ZU;2-T
Abstract
The Darboux method introduces algebraic solutions quite useful to obtain in variant and first integrals of polynomial differential systems. Here we stu dy the 2D Lotka-Volterra (LVS) and the complex quadratic system (QS) using straight lines for both and conics for the LVS. The conditions needed to ob tain these invariants are given and a study of the phase space portrait is done. (C) 1999 American Institute of Physics. [S0022-2488(99)02604-3].