Limit cycles of continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2023
Resum:	Due to their applications to many physical phenomena during these last decades the interest for studying the continuous or discontinuous piecewise differential systems has increased strongly. The limit cycles play a main role in the study of any planar differential system. Up to now the major part of papers which study the limit cycles of the planar piecewise differential systems have considered systems formed by two pieces separated by one straight line. Here we consider planar continuous piecewise differential systems separated by a parabola. We prove that the planar continuous piecewise differential systems separated by a parabola and formed by a linear center and a quadratic center have at most one limit cycle. Moreover there are systems in this class exhibiting one limit cycle. So in particular we have solved the extension of the 16th Hilbert problem to this class of differential systems.
Ajuts:	Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Continuous piecewise differential system ; Limit cycle ; Linear center ; Quadratic center
Publicat a:	Discrete and continuous dynamical systems. Series S, Vol. 16, Issue 3-4 (March-April 2023) , p. 533-547, ISSN 1937-1179

DOI: 10.3934/dcdss.2022034

Postprint 12 p, 805.3 KB

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