Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles

Author(s)

Novaes, Douglas D. ; Rondon, Gabriel

• Document type: Journal article
• Source: Nonlinearity; v. 34, n. 6, p. 4202-4263, JUN 2021.
• Web of Science Citations: 1

Abstract

Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in C ( n )-regularizations of Filippov systems around visible regular-tangential singularities of even multiplicity. More specifically, using Fenichel theory and blow-up methods, we aim to understand how the trajectories of the regularized system transits through the region of regularization. We apply our results to investigate C ( n )-regularizations of boundary limit cycles with even multiplicity contact with the switching manifold. (AU)

• FAPESP's process: 18/16430-8 - Global dynamics of nonsmooth differential equations
• Grantee: Douglas Duarte Novaes
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 20/06708-9 - Piecewise Holomorphic Systems and Regularization of Filippov fields around degenerated singularities and regular tangential polycycles
• Grantee: Gabriel Alexis Rondón Vielma
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants