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

Jaume Llibre; Clàudia Valls

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

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

Jaume Llibre, Clàudia Valls

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

35 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 language	English
Pages (from-to)	761-777
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	62
Issue number	5
DOIs	https://doi.org/10.1007/s00033-011-0119-2
Publication status	Published - 1 Oct 2011

Keywords

Analytic integrability
Lotka-Volterra systems
Polynomial integrability
Rational integrability

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

https://ddd.uab.cat/record/150436

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AU - Llibre, Jaume

AU - Valls, Clàudia

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N2 - 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.

AB - 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.

KW - Analytic integrability

KW - Lotka-Volterra systems

KW - Polynomial integrability

KW - Rational integrability

U2 - https://doi.org/10.1007/s00033-011-0119-2

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

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JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 5

ER -

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

Abstract

Keywords

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