On the crossing limit cycles for piecewise linear differential systems separated by a straight line and having symmetric equilibrium points
Jimenez Ruiz, Jeidy Johana (Universidade Federal do Oeste da Bahia)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Medrado, Joao Carlos (Universidade Federal de Goiás. Instituto de Matemática e Estatística)

Date:	2022
Abstract:	In this paper we study the maximum number of crossing limit cycles that can have the planar piecewise linear differential systems separated by a straight line Σ and formed by two linear differential systems X-, X+ which singularities are symmetrical with respect to the straight line of discontinuity Σ. More precisely, the singularities points of the linear differential systems X-, X+ considered can be a center (C), a focus (F), a diagonalizable node (N), an improper node (iN) or a saddle (S), which can be real or virtual. Then we have fourteen cases depending of the type and the position of the singularities of X- and X+. Here we provide lower or upper bounds for the maximum number of crossing limit cycles for each case.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Discontinuous piecewise linear differential centers ; Limit cycles ; Conics
Published in:	Dynamics of continuous, discrete and impulsive systems, Vol. 29, Num. 4b (2022) , p. 253-283, ISSN 1918-2538

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