Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

26 Citations (Scopus)

Abstract

We extend the study of the integrability done by Leach and Miritzis (J Nonlinear Math Phys 13:535-548, 2006) on the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29:243-256, 1975), to all real values of the parameters. Additionally, our results provide all polynomial, rational and analytic first integrals of this extended model. We also classify all the invariant algebraic surfaces of these models. © 2011 Springer Basel AG.
Original languageEnglish
Pages (from-to)761-777
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume62
Issue number5
DOIs
Publication statusPublished - 1 Oct 2011

Keywords

  • Analytic integrability
  • Lotka-Volterra systems
  • Polynomial integrability
  • Rational integrability

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