Bifurcations at a degenerate two-fold singularity and crossing limit cycles

Autor(es)

Cristiano, Rony ^[1] ; Pagano, Daniel J. ^[2] ; Carvalho, Tiago ^[3] ; Tonon, Durval J. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Goias, Inst Math & Stat, BR-74001970 Goiania, Go - Brazil

^[2] Univ Fed Santa Catarina, Dept Automat & Syst, BR-88040900 Florianopolis, SC - Brazil

^[3] Univ Sao Paulo, Fac Philosophy Sci & Letters Ribeirao Preto, Dept Computat & Math, BR-14040901 Ribeirao Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 268, n. 1, p. 115-140, DEC 15 2019.
• Citações Web of Science: 0

Resumo

In the 1990s Teixeira studied discontinuous piecewise-smooth (DPWS) dynamical systems in R-3, whose state space is divided in two open regions by a plane acting as the switching manifold, and presenting two lines of quadratic tangency, one for each involved vector field. We call T-singularity (Teixeira singularity) the point of transverse intersection of the quadratic tangency lines that are of the invisible type. In this paper, we analyze DPWS systems that present two branches of T-singularities. In our approach we consider the cases where either a pseudo-equilibrium collides to just one of the two T-singularities or the two T-singularities (and also a pseudo-equilibrium between them) collides in a single point. As a consequence of these bifurcations, until now not covered by the literature, we can observe the birth of limit cycles, determine their stability and provide an upper limit for the number of limit cycles that occur in this scenario. (C) 2019 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/00883-0 - Campos vetoriais suaves por partes com aplicações em problemas biológicos
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/02134-7 - Teoria qualitativa e bifurcações de campos de vetores suaves por partes
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular