Darboux integrability of polynomial differential systems in ℝ3

Jaume Llibre, Clàudia Valls

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Abstract

In this article we study the Darboux integrability of the polynomial differential systems x = y- x2, y; = z- x, z =-d- ax- by- cz. This system comes from the study of a Hopf bifurcation in slow-fast systems with two slow variables and one fast variable. The tools used here for studying the Darboux integrability can be applied to arbitrary polynomial differential systems in ℝ3.
Original languageEnglish
Pages (from-to)603-619
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume20
Issue number4
Publication statusPublished - 1 Jan 2013

Keywords

  • Darboux integrability
  • Darboux polynomial
  • Invariants

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