On the integrability of a tritrophic food chain model

Jaume Llibre; Clàudia Valls

doi:https://doi.org/10.1515/ans-2010-0206

On the integrability of a tritrophic food chain model

Jaume Llibre, Clàudia Valls

Department of Mathematics

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

Abstract

In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.

Original language	English
Pages (from-to)	331-355
Journal	Advanced Nonlinear Studies
Volume	10
Issue number	2
DOIs	https://doi.org/10.1515/ans-2010-0206
Publication status	Published - 1 Jan 2010

Keywords

Analytic integrability tritrophic food chain model
Darboux integrability
Darboux polynomial
Exponential factor
Formal integrability
Polynomial integrability

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https://doi.org/10.1515/ans-2010-0206

https://ddd.uab.cat/record/226091

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abstract = "In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.",

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AB - In this paper we work with a vastly analyzed tritrophic food chain model. We provide a complete characterization of their Darboux polynomials and of their exponential factors. We also show the non-existence of polynomial first integrals, of rational first integrals, of local analytic first integrals in a neighborhood of the origin, of first integrals that can be described by formal series and of Darboux first integrals.

KW - Analytic integrability tritrophic food chain model

KW - Darboux integrability

KW - Darboux polynomial

KW - Exponential factor

KW - Formal integrability

KW - Polynomial integrability

U2 - https://doi.org/10.1515/ans-2010-0206

DO - https://doi.org/10.1515/ans-2010-0206

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JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

SN - 1536-1365

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