The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems
Barkat, Meriem (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics)
Benterki, Rebiha (University Mohamed El Bachir El Ibrahimi of Bordj Bou Arréridj. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2023
Abstract:	In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems. This paper solves the extended 16th Hilbert problem for a family of discontinuous planar differential systems with two regions separated by the straight line x= 0. By using the first integrals, we prove that the maximum number of crossing limit cycles in the family of systems formed by a linear center and a class of Hamiltonian isochronous global center with a polynomial first integral of degree 2n is 5.
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 cycle ; Discontinuous piecewise linear differential systems ; Linear differential center ; Hamiltonian isochronous global center
Published in:	Nonlinear Dynamics, Vol. 111, Issue 2 (January 2023) , p. 1475-1484, ISSN 1573-269X

DOI: 10.1007/s11071-022-07891-9

Postprint 15 p, 350.7 KB

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