On the global flow of a 3-dimensional Lotka-Volterra system

Justino Alavez-Ramírez, Gamaliel Blé, Víctor Castellanos, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)


In the study of the black holes with a Higgs field appears in a natural way the Lotka-Volterra differential system ẋ=x(y-1),ẏ=y(1+y-2x 2-z 2),ż=zy, in ℝ 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify ℝ 3 with the interior of the unit ball of ℝ 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity. © 2012 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)4114-4125
JournalNonlinear Analysis, Theory, Methods and Applications
Publication statusPublished - 1 Jun 2012


  • Black hole
  • Higgs field
  • Lotka-Volterra system
  • Phase portrait
  • α-limit
  • ω-limit


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