Limit cycles of a continuous piecewise differential system formed by a quadratic center and two linear centers
Anacleto, Maria Elisa (Universidad del Bío-Bío. Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
Vidal, Claudio (Universidad del Bío-Bío. Departamento de Matemática)

Date:	2023
Abstract:	The study of limit cycles of planar differential systems is one of the main and difficult problems for understanding their dynamics. Thus the objective of this paper is to study the limit cycles of continuous piecewise differential systems in the plane separated by a non-regular line Σ. More precisely, we show that a class of continuous piecewise differential systems formed by an arbitrary quadratic center, an arbitrary linear center and the linear center x˙=-y,y˙=x have at most two crossing limit cycles and we find examples of such systems with one crossing limit cycle. So we have solved the extension of the 16th Hilbert problem to this class of piecewise differential systems providing an upper bound for its maximum number of limit cycles.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycles ; Linear center ; Quadratic center ; Continuous piecewise differential systems ; First integrals
Published in:	Boletin de la Sociedad Matematica Mexicana, Vol. 29, Issue 2 (July 2023) , art. 29, ISSN 2296-4495

DOI: 10.1007/s40590-023-00501-7

Available from: 2024-07-31 Postprint

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles