Limit cycles of polynomial Liénard systems via the averaging method
type: Item
instance of: scholarly article
title: Limit cycles of polynomial Liénard systems via the averaging method
zbMATH Open document ID: 1488.34228
author: Xianqiang Yang
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 7030124
zbMATH Keywords: polynomial Liénard system
zbMATH Keywords: limit cycle bifurcation
zbMATH Keywords: averaging method
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.07.030
OpenAlex ID: W2886955503
cites work: Q4135884
cites work: Uniqueness of limit cycles for Liénard differential equations of degree four
cites work: Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}]+2\) limit cycles
cites work: Slow divergence integrals in classical Liénard equations near centers
cites work: More limit cycles than expected in Liénard equations
cites work: Limit cycles of the generalized polynomial Liénard differential equations
cites work: Averaging theory at any order for computing periodic orbits
cites work: Bifurcation of limit cycles from a 4-dimensional center in \(\mathbb R^m\) in resonance \(1:N\)
cites work: Centers and limit cycles of polynomial differential systems of degree \(4\) via averaging theory
cites work: Averaging methods for finding periodic orbits via Brouwer degree.
cites work: New results on averaging theory and applications
cites work: Periodic solutions of the elliptic isosceles restricted three-body problem with collision by the averaging method
cites work: Limit cycles of cubic polynomial vector fields via the averaging theory
cites work: Averaging methods of arbitrary order, periodic solutions and integrability
cites work: On the limit cycles of planar polynomial system with non-rational first integral via averaging method at any order
cites work: On the periodic solutions of a class of Duffing differential equations
cites work: On the Hopf-zero bifurcation of the Michelson system
cites work: Equivalence of the Melnikov function method and the averaging method
cites work: On the equivalence of the Melnikov functions method and the averaging method
cites work: A theoretical basis for the Harmonic Balance Method
cites work: Upper bounds for the number of limit cycles through linear differential equations
cites work: On the determination of the limit cycles using the harmonic balance method
DOI: 10.1016/J.NONRWA.2018.07.030
description: scientific article; zbMATH DE number 7030124