Cardoso, Joao L.
Novaes, Douglas D.
Tonon, Durval J.
Número total de Autores: 4
Afiliação do(s) autor(es):
 Univ Fed Goias, Inst Math & Stat, Goiania, Go - Brazil
 Univ Autonoma Barcelona, Dept Matemat, Barcelona, Catalonia - Spain
 Univ Estadual Campinas, Dept Matemat, Sao Paulo - Brazil
Número total de Afiliações: 3
Tipo de documento:
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL;
Citações Web of Science:
In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for yy>0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation. (AU)