Limit cycles for a class of third-order differential equations

Jaume Llibre; Jiang Yu; Xiang Zhang

doi:10.1216/RMJ-2010-40-2-581

Limit cycles for a class of third-order differential equations

Jaume Llibre, Jiang Yu, Xiang Zhang

Department of Mathematics

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

10 Citations (Scopus)

Abstract

In this paper we study the limit cycles of the third-order differential equation x - μẍ + ẋ - μx = εF(x, ẋ, ẍ, t), where μ ≠ 0, ε is small enough and F ∈ C2 is a 2π-periodic function of variable t. Copyright ©2010 Rocky Mountain Mathematics Consortium.

Original language	English
Pages (from-to)	581-594
Journal	Rocky Mountain Journal of Mathematics
Volume	40
Issue number	2
DOIs	https://doi.org/10.1216/RMJ-2010-40-2-581
Publication status	Published - 1 Jul 2010

Keywords

Averaging theory
Limit cycle
Perturbation of centers
Third-order differential equation

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10.1216/RMJ-2010-40-2-581

https://ddd.uab.cat/record/226102

Cite this

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title = "Limit cycles for a class of third-order differential equations",

abstract = "In this paper we study the limit cycles of the third-order differential equation x - μẍ + ẋ - μx = εF(x, ẋ, ẍ, t), where μ ≠ 0, ε is small enough and F ∈ C2 is a 2π-periodic function of variable t. Copyright {\textcopyright}2010 Rocky Mountain Mathematics Consortium.",

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AU - Llibre, Jaume

AU - Yu, Jiang

AU - Zhang, Xiang

PY - 2010/7/1

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N2 - In this paper we study the limit cycles of the third-order differential equation x - μẍ + ẋ - μx = εF(x, ẋ, ẍ, t), where μ ≠ 0, ε is small enough and F ∈ C2 is a 2π-periodic function of variable t. Copyright ©2010 Rocky Mountain Mathematics Consortium.

AB - In this paper we study the limit cycles of the third-order differential equation x - μẍ + ẋ - μx = εF(x, ẋ, ẍ, t), where μ ≠ 0, ε is small enough and F ∈ C2 is a 2π-periodic function of variable t. Copyright ©2010 Rocky Mountain Mathematics Consortium.

KW - Averaging theory

KW - Limit cycle

KW - Perturbation of centers

KW - Third-order differential equation

UR - https://www.scopus.com/pages/publications/77953985279

U2 - 10.1216/RMJ-2010-40-2-581

DO - 10.1216/RMJ-2010-40-2-581

M3 - Article

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VL - 40

SP - 581

EP - 594

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 2

ER -

Limit cycles for a class of third-order differential equations

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Keywords

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