Alien limit cycles in Abel equations
type: Item
instance of: scholarly article
title: Alien limit cycles in Abel equations
zbMATH Open document ID: 1434.34035
author: Yanyan Li
published in: Journal of Mathematical Analysis and Applications
publication date: 2019-11-28T00:00:00Z
review text: The authors consider the generalized Abel equation \[ \frac{dx}{dt}=\left(a_{1}A_{1}(t)+a_{2}A_{2}(t)\right)x^m+\left(a_{3}A_{3}(t)+a_{4}A_{4}(t)\right)x^n, \] where \(t, {a}_{i}\in \mathbb{R}\), \(i=\overline{1,4}\); \(m, n\in \mathbb{N}\), \(m>n\ge 2\). Sufficient conditions are obtained under which the generalized Abel equation has a so-called alien limit cycle, i.e., limit cycle that arises from neither a Hopf bifurcation nor a perturbation of periodic orbits in a period annulus around the centre at the origin.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C08
zbMATH DE Number: 7138382
zbMATH Keywords: periodic solutions
zbMATH Keywords: Abel equation
zbMATH Keywords: alien limit cycles
zbMATH Keywords: abelian integrals
zbMATH Keywords: bifurcation
reviewed by: Èduard V. Musafirov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2019.123525
OpenAlex ID: W2976651471
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Wikidata QID: Q127218690
DOI: 10.1016/J.JMAA.2019.123525
description: scientific article; zbMATH DE number 7138382