Quadratic systems with limit cycles of normal size
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CHERKAS, Leonid; ARTES, Joan; LLIBRE, Jaume. Quadratic systems with limit cycles of normal size. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2003, nr. 1(41), pp. 31-46. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 1(41) / 2003 / ISSN 1024-7696

Quadratic systems with limit cycles of normal size

Pag. 31-46

Cherkas Leonid, Artes Joan, Llibre Jaume
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 13 decembrie 2013


Rezumat

In the class of planar autonomous quadratic polynomial differential sys- tems 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 hav- ing 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 Du- lac 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.

Cuvinte-cheie
quadratic systems, limit cycles.