Quadratic perturbations of a quadratic reversible Lotka-Volterra system

Chengzhi Li; Jaume Llibre

doi:10.1007/s12346-010-0026-5

Quadratic perturbations of a quadratic reversible Lotka-Volterra system

Chengzhi Li, Jaume Llibre

Department of Mathematics

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

11 Citations (Scopus)

Abstract

We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0, 0), (1, 0), (2, 0), (1, 1) and (1, 2). © Springer Basel AG 2010.

Original language	English
Pages (from-to)	235-249
Journal	Qualitative Theory of Dynamical Systems
Volume	9
Issue number	1-2
DOIs	https://doi.org/10.1007/s12346-010-0026-5
Publication status	Published - 1 Jan 2010

Keywords

Averaging theory
Isochronous center
Limit cycles
Quadratic vector field

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abstract = "We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system{\. }x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0, 0), (1, 0), (2, 0), (1, 1) and (1, 2). {\textcopyright} Springer Basel AG 2010.",

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AU - Llibre, Jaume

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N2 - We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0, 0), (1, 0), (2, 0), (1, 1) and (1, 2). © Springer Basel AG 2010.

AB - We prove that perturbing the two periodic annuli of the quadratic polynomial reversible Lotka-Volterra differential system ̇x = -y + x2 - y2, ẏ = x(1 + 2y), inside the class of all quadratic polynomial differential systems we can obtain the following configurations of limit cycles (0, 0), (1, 0), (2, 0), (1, 1) and (1, 2). © Springer Basel AG 2010.

KW - Averaging theory

KW - Isochronous center

KW - Limit cycles

KW - Quadratic vector field

U2 - 10.1007/s12346-010-0026-5

DO - 10.1007/s12346-010-0026-5

M3 - Article

VL - 9

SP - 235

EP - 249

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

SN - 1575-5460

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