Cyclicity of  some Liénard Systems

Na  Li; Maoan Han; Valery G.  Romanovski

doi:10.3934/cpaa.2015.14.2127

Article Contents

2015, Volume 14, Issue 6: 2127-2150. Doi: 10.3934/cpaa.2015.14.2127

This issue Previous Article Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane Next Article Homogenization of bending theory for plates; the case of oscillations in the direction of thickness

Cyclicity of some Liénard Systems

1.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234

Received: March 2014

Revised: June 2015

Published: November 2015

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Abstract

The Liénard system and its generalizations are important models of nonlinear oscillators. We study small-amplitude limit cycles of two families of Liénard systems and find exact number of such limit cycles bifurcating from a center or focus at the origin for these families, thus obtaining the precise bound for cyclicity of the families.

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

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