Weak focus, limit cycles, and bifurcations for bounded quadratic systems
type: Item
instance of: scholarly article
title: Weak focus, limit cycles, and bifurcations for bounded quadratic systems
zbMATH Open document ID: 0823.34043
author: Chengzhi Li
author: Jaume Llibre
author: Zhifen Zhang
published in: Journal of Differential Equations
publication date: 1995-01-30T00:00:00Z
review text: This paper is an interesting contribution to the qualitative study of two-dimensional autonomous ordinary differential equations. For quadratic nonlinearities, the global phase portrait (i.e. taking into account the Poincaré's equator), and its qualitative changes when the parameters equation vary, are studied. It is a pity that the authors do not refer in this field to the fundamental and ancient contribution of the ``Andronov School''. Indeed, the books and papers on the qualitative theory of dynamical systems of Andronov, Gordon, Mayer, Leontovitch, Bautin, have considered equivalent (but not the same) problems from 1939 to 1976. It is particularly the case of the excellent book ``Methods and applications of the qualitative study of the dynamical systems in the plane'', Nauka, Moscow, 1976, written by \textit{N. N. Bautin} and \textit{E. A. Leontovitch}.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 714693
zbMATH Keywords: two-dimensional autonomous ordinary differential equations
zbMATH Keywords: quadratic nonlinearities
zbMATH Keywords: global phase portrait
reviewed by: Christian Mira
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1012
OpenAlex ID: W2030527508
DOI: 10.1006/JDEQ.1995.1012
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description: scientific article; zbMATH DE number 714693