The Solution of the Extended 16th Hilbert Problem for Some Classes of Piecewise Differential Systems
Baymout, Louiza (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj)
Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2024
Resum:	The limit cycles have a main role in understanding the dynamics of planar differential systems, but their study is generally challenging. In the last few years, there has been a growing interest in researching the limit cycles of certain classes of piecewise differential systems due to their wide uses in modeling many natural phenomena. In this paper, we provide the upper bounds for the maximum number of crossing limit cycles of certain classes of discontinuous piecewise differential systems (simply PDS) separated by a straight line and consequently formed by two differential systems. A linear plus cubic polynomial forms six families of Hamiltonian nilpotent centers. First, we study the crossing limit cycles of the PDS formed by a linear center and one arbitrary of the six Hamiltonian nilpotent centers. These six classes of PDS have at most one crossing limit cycle, and there are systems in each class with precisely one limit cycle. Second, we study the crossing limit cycles of the PDS formed by two of the six Hamiltonian nilpotent centers. There are systems in each of these 21 classes of PDS that have exactly four crossing limit cycles.
Ajuts:	European Commission 777911 Agencia Estatal de Investigación PID2019-104658GB-I00
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Discontinuous piecewise differential system ; Hamiltonian nilpotent center ; Cubic polynomial differential system ; Limit cycle ; Vector field
Publicat a:	Mathematics, Vol. 12, Issue 3 (February 2024) , art. 464, ISSN 2227-7390

DOI: 10.3390/math12030464

29 p, 757.3 KB

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