The limit cycles of a class of discontinuous piecewise differential systems
Baymout, Louiza (Université Mohamed El Bachir El Ibrahimi. Département de mathématiques)
Benterki, Rebiha (Université Mohamed El Bachir El Ibrahimi. Département de mathématiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	The determination of the maximum number of limit cycles and their possible positions in the plane is one of the most difficult problems in the qualitative theory of planar differential systems. This problem is related to the second part of the unsolved 16th Hilbert's problem. Due to their applications in modelling many natural phenomena, piecewise differential systems have recently attracted big attention. The upper bound number of limit cycles that a class of differential systems may exhibit is typically very difficult to determine. In this work we extend the second part of the 16th Hilbert's problem to the planar discontinuous piecewise differential systems separated by a straight line and formed by an arbitrary linear centre and an arbitrary cubic uniform isochronous centre. We provide for this class of piecewise differential systems an upper bound on its maximal number of limit cycles, and we prove that such an upper bound is reached.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: Reial Acadèmia de Ciències i Arts de Barcelona
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Cubic uniform isochronous centre ; Linear centre ; Limit cycle ; Discontinuous piecewise differential system
Published in:	International Journal of Dynamical Systems and Differential Equations, Vol. 13, Issue 4 (2024) , p. 339-368, ISSN 1752-3591

DOI: 10.1504/IJDSDE.2024.144873

Available from: 2026-03-31 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