Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/2898
Title: Local bifurcations and a survey of bounded quadratic systems
Authors: DUMORTIER, Freddy 
HERSSENS, Chris 
Perko, L
Issue Date: 2000
Publisher: ACADEMIC PRESS INC
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 165(2). p. 430-467
Abstract: This paper presents a survey of the known results for bounded quadratic systems as well as a study of the local bifurcations that occur at critical points of such systems. It is shown that the only finite-codimension bifurcations that occur at a critical point of a bounded quadratic system are the saddle-node and the Hopf-Takens bifurcations of codimensions 1 and 2 and the Bogdanov-Takens bifurcations of codimensions 2 and 3; furthermore, it is shown that whenever a bounded quadratic system has one of these critical points, then a full generic unfolding of the critical point exists in the class of bounded quadratic systems. Finally, we give a complete list of those limit periodic sets whose finite cyclicity still needs to be established in order to obtain the existence of a finite upper bound for the number of limit cycles that can occur in a hounded quadratic system. (C) 2000 Academic Press.
Notes: Limburgs Univ Ctr, B-3610 Diepenbeek, Belgium. No Arizona Univ, Flagstaff, AZ 86011 USA.Dumortier, F, Limburgs Univ Ctr, Univ Campus, B-3610 Diepenbeek, Belgium.
Document URI: http://hdl.handle.net/1942/2898
DOI: 10.1006/jdeq.2000.3777
ISI #: 000088679600006
Category: A1
Type: Journal Contribution
Validations: ecoom 2001
Appears in Collections:Research publications

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