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

Laurent Cairó; Marc R. Feix; Jaume Llibre

doi:10.1063/1.532852

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

Laurent Cairó, Marc R. Feix, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

21 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 language	English
Pages (from-to)	2074-2091
Journal	Journal of Mathematical Physics
Volume	40
Issue number	4
DOIs	https://doi.org/10.1063/1.532852
Publication status	Published - 1 Jan 1999

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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. {\textcopyright} 1999 American Institute of Physics.",

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AB - 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.

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

Abstract

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