Limit cycles of some polynomial Liénard systems

Weijiao Xu; Cuiping Li

doi:10.1016/j.jmaa.2011.11.070

Limit cycles of some polynomial Liénard systems

Weijiao Xu^*
, Cuiping Li

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

28 Scopus citations

Abstract

In this paper, we study the number of limit cycles of some polynomial Liénard systems. By the Melnikov functions and the methods of Hopf, homoclinic and heteroclinic bifurcation theory, we prove that H(2, 5) ≥ 3, H(4, 5) ≥ 5, H(6, 5) ≥ 10, H(8, 5) ≥ 10.

Original language	English
Pages (from-to)	367-378
Number of pages	12
Journal	Journal of Mathematical Analysis and Applications
Volume	389
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.11.070
State	Published - 1 May 2012

Keywords

Heteroclinic loop
Homoclinic loop
Liénard system
Melnikov function

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10.1016/j.jmaa.2011.11.070

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title = "Limit cycles of some polynomial Li{\'e}nard systems",

abstract = "In this paper, we study the number of limit cycles of some polynomial Li{\'e}nard systems. By the Melnikov functions and the methods of Hopf, homoclinic and heteroclinic bifurcation theory, we prove that H(2, 5) ≥ 3, H(4, 5) ≥ 5, H(6, 5) ≥ 10, H(8, 5) ≥ 10.",

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author = "Weijiao Xu and Cuiping Li",

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doi = "10.1016/j.jmaa.2011.11.070",

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AU - Li, Cuiping

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AB - In this paper, we study the number of limit cycles of some polynomial Liénard systems. By the Melnikov functions and the methods of Hopf, homoclinic and heteroclinic bifurcation theory, we prove that H(2, 5) ≥ 3, H(4, 5) ≥ 5, H(6, 5) ≥ 10, H(8, 5) ≥ 10.

KW - Heteroclinic loop

KW - Homoclinic loop

KW - Liénard system

KW - Melnikov function

UR - https://www.scopus.com/pages/publications/84855840408

U2 - 10.1016/j.jmaa.2011.11.070

DO - 10.1016/j.jmaa.2011.11.070

M3 - 文章

AN - SCOPUS:84855840408

SN - 0022-247X

VL - 389

SP - 367

EP - 378

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Limit cycles of some polynomial Liénard systems

Abstract

Keywords

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