Uniqueness of limit cycles of quadratic system (III)\(_{m=0}\)
type: Item
instance of: scholarly article
title: Uniqueness of limit cycles of quadratic system (III)\(_{m=0}\)
zbMATH Open document ID: 0883.34036
DOI: 10.1007/BF03182636
author: Xiang Zhang
author: Qin Ye
published in: Chinese Science Bulletin
publication date: 1998-03-16T00:00:00Z
review text: By using a theorem on the uniqueness of limit cycles due to W. A. Coppel the authors prove the following theorem: Under the conditions: \[ a<0,\;\ell> {1\over 2},\;0<n<1,\;\delta<0 \] the quadratic system \(\text{(III)}_{m=0}\) (Chinese classification) \[ \dot x=-y +\delta x+ \ell x^2+ny^2, \quad \dot y= x(1+ax-y) \] has at most one limit cycle. If it exists, it must be hyperbolic and unstable.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1066756
zbMATH Keywords: uniqueness
zbMATH Keywords: limit cycles
zbMATH Keywords: quadratic system
reviewed by: Yanqian Ye
MaRDI profile type: Publication
cites work: Q4715040
cites work: Q3972439
cites work: Q4036054
cites work: A new class of quadratic systems
cites work: Q3798988
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description: scientific article; zbMATH DE number 1066756