The cyclicity of the period annulus of a class of quadratic reversible system

Yi Shao; Yulin Zhao

doi:10.3934/cpaa.2012.11.1269

Article Contents

2012, Volume 11, Issue 3: 1269-1283. Doi: 10.3934/cpaa.2012.11.1269

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The cyclicity of the period annulus of a class of quadratic reversible system

Yi Shao^1, and
Yulin Zhao^2,

1.
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275
2.
Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275

Received: November 30, 2010

Revised: February 28, 2011

Published: April 2012

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Abstract

In this paper, we study the bifurcation of limit cycles of a class of planar quadratic reversible system $\dot{x}=y+4x^2$, $\dot{y}=-x+2xy$ under quadratic perturbations. It is proved that the cyclicity of the period annulus is equal to two.

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Mathematics Subject Classification: Primary: 34C07, 34C10; Secondary: 37G15.

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