On cyclicity of triangles and segments in quadratic systems
type: Item
instance of: scholarly article
title: On cyclicity of triangles and segments in quadratic systems
zbMATH Open document ID: 0840.34031
author: Henryk Żołądek
published in: Journal of Differential Equations
publication date: 1996-07-09T00:00:00Z
review text: This paper deals with bifurcations, and limit cycles properties of a family of two-dimensional autonomous ordinary differential equations defined by two quadratic functions. A ``generator'' (or non perturbated) quadratic system, having three invariant lines (the two axes and an oblique line), is considered. It is perturbated by quadratic terms. Different situations of the generator system called ``bounded triangle'', ``unbounded triangle'', and the limit cases ``line at infinite case'' ``double invariant line case'', plus the Hamiltonian case, are studied. Other situations denoted ``bounded segments'', and ``unbounded segments'' are indicated. It is shown that after perturbation the maximal number of limit cycles is three for the bounded triangle case, and two for the unbounded triangle, one for the bounded segment.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 810066
zbMATH Keywords: periodic solutions
zbMATH Keywords: bifurcations
zbMATH Keywords: maximal number of limit cycles
reviewed by: Christian Mira
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1142
OpenAlex ID: W2062487396
DOI: 10.1006/JDEQ.1995.1142
description: scientific article; zbMATH DE number 810066