Limit cycles for a class of third-order differential equations
type: Item
instance of: scholarly article
title: Limit cycles for a class of third-order differential equations
zbMATH Open document ID: 1196.37087
DOI: 10.1216/RMJ-2010-40-2-581
author: Jiang Yu
author: Xiang Zhang
author: Jaume Llibre
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-06-14T00:00:00Z
review text: The authors study the limit cycles of the following class of third-order ordinary differential equations \[ \dddot{x}-\mu\ddot{x}+\dot{x}-\mu x=\varepsilon F(x,\dot{x},\ddot{x},t) \] where \(\mu \neq 0\), and the dot means derivative with respect to variable \(t\), \(\varepsilon\) is small enough and \(F\in \mathcal{C}^2\) is a \(2\pi\)-periodic function of variable \(t\). The variables \(x\) and \(t\), and parameters \(\mu\) and \(\varepsilon\) are real.
reviewed by: Irina V. Konopleva
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5720622
zbMATH Keywords: limit cycle
zbMATH Keywords: third-order differential equation
zbMATH Keywords: perturbation of centers
zbMATH Keywords: averaging theory
MaRDI profile type: Publication
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full work available at URL: rmj-2010-40-2-581
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description: scientific article; zbMATH DE number 5720622