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IMCS/Publications/BASM/Issues/BASM n.1 (41), 2003/

Quadratic systems with limit cycles of normal size. (English)

Authors: Leonid A. Cherkas, Joan C. Artes, Jaume Llibre.

Abstract

In the class of planar autonomous quadratic polynomial differential systems we provide 6 different phase portraits having exactly 3 limit cycles surrounding a focus, 5 of them have a unique focus. We also provide 2 different phase portraits having exactly 3 limit cycles surrounding one focus and 1 limit cycle surrounding another focus. The existence of the exact given number of limit cycles is proved using the Dulac function. All limit cycles of the given systems can be detected through numerical methods; i.e. the limit cycles have "a normal size" using Perko's terminology.

Leonid A. Cherkas
Belarusian State University of Informatics and Radioelectronics
Minsk, 220027 Belarus
E-mail:
Joan C. Artes and Jaume Llibre
Departament de Matematiques
Universitat Autonoma de Barcelona Bellaterra,
08193 Barcelona,
E-mail:
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