Limit cycles of a second-order differential equation

Ting Chen; Jaume Llibre

doi:https://doi.org/10.1016/j.aml.2018.08.015

Limit cycles of a second-order differential equation

Ting Chen, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research

1 Citation (Scopus)

Abstract

© 2018 Elsevier Ltd We provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of ẍ+x=0, when we perturb this system as follows ẍ+ε(1+cosmθ)Q(x,y)+x=0,where ε>0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and θ=arctan(y∕x). The main tool used for proving our results is the averaging theory.

Original language	English
Pages (from-to)	111-117
Journal	Applied Mathematics Letters
Volume	88
DOIs	https://doi.org/10.1016/j.aml.2018.08.015
Publication status	Published - 1 Feb 2019

Keywords

Averaging theory
Limit cycle
Mathieu–Duffing type

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AB - © 2018 Elsevier Ltd We provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of ẍ+x=0, when we perturb this system as follows ẍ+ε(1+cosmθ)Q(x,y)+x=0,where ε>0 is a small parameter, m is an arbitrary non-negative integer, Q(x,y) is a polynomial of degree n and θ=arctan(y∕x). The main tool used for proving our results is the averaging theory.

KW - Averaging theory

KW - Limit cycle

KW - Mathieu–Duffing type

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