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

Laurent Cairó, Marc R. Feix, Jaume Llibre

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19 Citations (Scopus)

Abstract

The Darboux method introduces algebraic solutions quite useful to obtain invariant and first integrals of polynomial differential systems. Here we study 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 obtain these invariants are given and a study of the phase space portrait is done. © 1999 American Institute of Physics.
Original languageEnglish
Pages (from-to)2074-2091
JournalJournal of Mathematical Physics
Volume40
Issue number4
DOIs
Publication statusPublished - 1 Jan 1999

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