On the dynamics of a class of Kolmogorov systems

Jaume Llibre; Tayeb Salhi

doi:https://doi.org/10.1016/j.amc.2013.09.017

On the dynamics of a class of Kolmogorov systems

Jaume Llibre, Tayeb Salhi

Department of Mathematics

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

19 Citations (Scopus)

Abstract

We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the formxÌ‡=x( Pn(x,y)+Rm(x,y)),yÌ‡=y(Qn(x,y) +Rm(x,y)),where n and m are positive integers and Pn, Qn and Rm are homogeneous polynomials of degree n,n and m, respectively. © 2013 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	242-245
Journal	Applied Mathematics and Computation
Volume	225
DOIs	https://doi.org/10.1016/j.amc.2013.09.017
Publication status	Published - 29 Oct 2013

Keywords

Integrability
Kolmogorov systems
Lotka-Volterra systems
Periodic orbits

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title = "On the dynamics of a class of Kolmogorov systems",

abstract = "We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the formx{\`I}‡=x( Pn(x,y)+Rm(x,y)),y{\`I}‡=y(Qn(x,y) +Rm(x,y)),where n and m are positive integers and Pn, Qn and Rm are homogeneous polynomials of degree n,n and m, respectively. {\textcopyright} 2013 Elsevier Inc. All rights reserved.",

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author = "Jaume Llibre and Tayeb Salhi",

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AU - Llibre, Jaume

AU - Salhi, Tayeb

PY - 2013/10/29

Y1 - 2013/10/29

N2 - We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the formxÌ‡=x( Pn(x,y)+Rm(x,y)),yÌ‡=y(Qn(x,y) +Rm(x,y)),where n and m are positive integers and Pn, Qn and Rm are homogeneous polynomials of degree n,n and m, respectively. © 2013 Elsevier Inc. All rights reserved.

AB - We characterize the integrability and the non-existence of periodic orbits for the 2-dimensional Kolmogorov systems of the formxÌ‡=x( Pn(x,y)+Rm(x,y)),yÌ‡=y(Qn(x,y) +Rm(x,y)),where n and m are positive integers and Pn, Qn and Rm are homogeneous polynomials of degree n,n and m, respectively. © 2013 Elsevier Inc. All rights reserved.

KW - Integrability

KW - Kolmogorov systems

KW - Lotka-Volterra systems

KW - Periodic orbits

U2 - https://doi.org/10.1016/j.amc.2013.09.017

DO - https://doi.org/10.1016/j.amc.2013.09.017

M3 - Article

SN - 0096-3003

VL - 225

SP - 242

EP - 245

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

On the dynamics of a class of Kolmogorov systems

Abstract

Keywords

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