Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves

• Autorzy: Benterki Rebiha , Belfar Ahlam

Identyfikatory

DOI

10.1515/dema-2022-0218

• Języki publikacji: EN

Abstrakty

EN

The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R2, particularly for quadratic systems. Even with the hundreds of studies on the topology of real planar quadratic vector fields, fully characterizing their phase portraits is still a difficult problem. This paper is devoted to classifying the phase portraits of two polynomial vector fields with two usual invariant algebraic curves, by investigating the geometric solutions within the Poincaré disc. One can notice that these systems yield 26 topologically different phase portraits.

Słowa kluczowe

EN

polynomial vector fields; phase portrait; invariant curve

PL

pola wektorowe; portret fazowy; niezmiennicza krzywa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220218
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Benterki Rebiha

• Department of Mathematics, Mathematical Analysis and Applications Laboratory, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj 34030, El Anasser, Algeria

autor

Belfar Ahlam

• Department of Mathematics, Mathematical Analysis and Applications Laboratory, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj 34030, El Anasser, Algeria

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).