Quadratic systems with limit cycles of normal size

Cherkas Leonid; Artes Joan; Llibre Jaume

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991

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2020-07-01 09:25

SM ISO690:2012

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

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 1(41) / 2003 / ISSN 1024-7696 /ISSNe 2587-4322

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

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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.

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