The generic unfolding of a codimension-two connection to a two-fold singularity of planar Filippov systems

Author(s)

Novaes, Douglas D. ^[1] ; Teixeira, Marco A. ^[1] ; Zeli, Iris O. ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Nonlinearity; v. 31, n. 5, p. 2083-2104, MAY 2018.
• Web of Science Citations: 1

Abstract

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector fields. In the present study we focus on a qualitative analysis of 2-parameter families, Z(alpha,beta), of planar Filippov systems assuming that Z(0,0) presents a codimension-two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the first return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram. (AU)

• FAPESP's process: 16/11471-2 - Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Regular Research Grants
• FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/21078-8 - Periodic solutions dor discontinuous dynamical systems with symmetry
• Grantee: Iris de Oliveira Zeli
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 12/23591-1 - Singularities theory on dynamical systems in presence of symmetry
• Grantee: Iris de Oliveira Zeli
• Support Opportunities: Scholarships in Brazil - Post-Doctoral