Limit Cycles of the Discontinuous Piecewise Differential Systems Separated by a Nonregular Line and Formed by a Linear Center and a Quadratic One
Baymout, Louiza (University Mohamed El Bachir. Department of Mathematics)
Benterki, Rebiha (University Mohamed El Bachir. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	During the last decades, the study of discontinuous piecewise differential systems has become an interesting subject of research due to the important applications of this kind of systems to model natural phenomena. In the qualitative theory of differential equations, one of the interesting problems is the detection of the number of limit cycles and their configurations which remains open to date, except for very particular families of differential equations. Here, we are inspired to study the maximum number of limit cycles of the discontinuous piecewise differential systems separated by a nonregular line and formed by a linear center and one of the four classes of quadratic centers. The main tool used to prove our main results is based on the first integrals of such systems. All the computations of this paper are verified using the algebraic manipulator Mathematica.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Rights:	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.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Quadratic center ; Linear center ; Limit cycle ; Discontinuous piecewise differential system
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 34, Issue 5 (April 2024) , art. 2450058, ISSN 1793-6551

DOI: 10.1142/S0218127424500585

Postprint 41 p, 1.3 MB

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