Maximum number of limit cycles for certain piecewise linear dynamical systems

Autor(es)

Llibre, Jaume ^[1] ; Novaes, Douglas D. ^[2] ; Teixeira, Marco A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 82, n. 3, p. 1159-1175, NOV 2015.
• Citações Web of Science: 13

Resumo

This paper deals with the question of the determinacy of the maximum number of limit cycles of some classes of planar discontinuous piecewise linear differential systems defined in two half-planes separated by a straight line . We restrict ourselves to the non-sliding limit cycles case, i.e., limit cycles that do not contain any sliding segment. Among all cases treated here, it is proved that the maximum number of limit cycles is at most 2 if one of the two linear differential systems of the discontinuous piecewise linear differential system has a focus in , a center, or a weak saddle. We use the theory of Chebyshev systems for establishing sharp upper bounds for the number of limit cycles. Some normal forms are also provided for these systems. (AU)

• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/10231-7 - Regularização e conjuntos minimais para sistemas dinâmicos não suaves
• Beneficiário: Douglas Duarte Novaes
• Modalidade de apoio: Bolsas no Brasil - Doutorado