Dynamics of a Lotka-Volterra map

Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

Given the plane triangle with vertices (0, 0), (0, 4) and (4, 0) and the transformation F : (x, y) → (x(4 - x - y), xy) introduced by A. N. Sharkovskiǐ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior of the Schrödinger equation.
Original languageEnglish
Pages (from-to)265-279
JournalFundamenta Mathematicae
Volume191
DOIs
Publication statusPublished - 13 Nov 2006

Keywords

  • Periodic trajectory
  • Resultant
  • Spiral type curve

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