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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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