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

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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.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, Instituto Superior Técnico, 1049–001, Lisbon, Portugal

    Clàudia Valls

Authors
  1. Jaume Llibre
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  2. Clàudia Valls
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Correspondence to Jaume Llibre.

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Llibre, J., Valls, C. Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems. Z. Angew. Math. Phys. 62, 761–777 (2011). https://doi.org/10.1007/s00033-011-0119-2

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  • DOI: https://doi.org/10.1007/s00033-011-0119-2

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