Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field

Author(s)

Carvalho, Tiago ; Euzebio, Rodrigo D. ; Teixeira, Marco Antonto ; Tonon, Durval Jose

• Document type: Journal article
• Source: IMA JOURNAL OF APPLIED MATHEMATICS; v. 82, n. 3, p. 561-578, JUN 2017.
• Web of Science Citations: 0

Abstract

We consider a piecewise smooth vector field in R-3, where the switching set is on an algebraic variety expressed as the zero of a Morse function. We depart from a model described by piecewise constant vector fields with a non-usual center that is constant on the sliding region. Given a positive integer k, we produce suitable nonlinear small perturbations of the previous model and we obtain piecewise smooth vector fields having exactly k hyperbolic limit cycles instead of the center. Moreover, we also obtain suitable nonlinear small perturbations of the first model and piecewise smooth vector fields having a unique limit cycle of multiplicity k instead of the center. As consequence, the initial model has codimension infinity. Some aspects of asymptotical stability of such system are also addressed in this article. (AU)

• FAPESP's process: 14/18508-3 - Minimal sets of piecewise differential systems in dimension 3
• Grantee: Rodrigo Donizete Euzébio
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems
• Grantee: Rodrigo Donizete Euzébio
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 14/02134-7 - Qualitative theory and bifurcations of piecewise smooth vector fields
• Grantee: Tiago de Carvalho
• Support Opportunities: Regular Research Grants