A simple class of quadratic systems
type: Item
instance of: scholarly article
title: A simple class of quadratic systems
zbMATH Open document ID: 0603.34023
DOI: 10.1016/0022-0396(86)90075-6
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: The author, using ideas of \textit{A. L. Neto} [Invent. Math. 59, 67-76 (1980; Zbl 0448.34012)], shows that a plane quadratic system with only one finite critical point and one critical point at infinity, has at most one limit cycle. This generalizes and simplifies work of \textit{D. E. Koditschek} and \textit{K. S. Narendra} [J. Differ. Equations 54, 181-195 (1984; Zbl 0498.34018)], originating in control theory. Subsequently Boll, Gasull and Llibre [preprint, Barcelona] have determined all cases in which Neto's method may be applied. (They have also pointed out that the description of the phase portrait in the author's case (ii) requires modification.)
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G15
zbMATH DE Number: 3973338
zbMATH Keywords: quadratic system
zbMATH Keywords: plane quadratic system
zbMATH Keywords: critical point
zbMATH Keywords: limit cycle
author: William Andrew Coppel
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90075-6
OpenAlex ID: W1979949102
cites work: Q4768040
cites work: Q5615538
cites work: Limit cycles of a class of polynomial vector fields in the plane
cites work: On General Properties of Quadratic Systems
cites work: A survey of quadratic systems
cites work: Bounded quadratic systems in the plane
cites work: Limit cycles of planar quadratic differential equations
cites work: On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
cites work: Existence, uniqueness, and nonexistence of limit cycles for a class of quadratic systems in the plane
cites work: Q5529795
cites work: Q3957244
cites work: Q3310965
cites work: Number of limit cycles of the bounded quadratic system with two finite singular points
cites work: Some problems in the qualitative theory of ordinary differential equations
description: scientific article; zbMATH DE number 3973338