On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems

Autor:	Aziza Berbache
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	discontinuous piecewise differential system continuous piecewise differential system first integral non-algebraic limit cycle linear system quadratic center Mathematics QA1-939
Zdroj:	Mathematica Bohemica, Vol 148, Iss 4, Pp 617-629 (2023)
Druh dokumentu:	article
ISSN:	0862-7959 2464-7136
DOI:	10.21136/MB.2022.0181-21
Popis:	We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we have solved the extension of the 16th Hilbert problem to this class of differential systems.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/439db790a58c4107b909850694ea5a5b Zobrazit plný text záznamu View record in DOAJ