Bifurcation of piecewise smooth systems with singular borders via regularization

• Grant number: 16/00242-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2016
• End date: January 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Yagor Romano Carvalho
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM
• Associated scholarship(s): 18/05098-2 - Study of limit cycles in piecewise smooth systems on the cylinder, BE.EP.DR

Abstract

The proposal is devoted to the study of piecewise smooth vector fields, in the case where the border of the smooth parts of the vector fields are not regular. In this context, it will be first made a study aimed at a classification of systems that are not structurally stable. Necessarily such a study requires an analysis of bifurcations of low codimension 1 and 2. Finally the project will be completed with an analysis of the regularization of the systems studied in the previous steps. To accomplish this last step will be necessary to develop a generalization of Sotomayor and Teixeira method for the singular case.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BUZZI, CLAUDIO A.; ROMANO CARVALHO, YAGOR; GASULL, ARMENGOL. Limit cycles for some families of smooth and non-smooth planar systems. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 207, JUN 2021. (16/00242-2, 18/05098-2, 19/10269-3)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; LLIBRE, JAUME. Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 37, n. 4, p. 19-pg., 2022-09-28. (21/14695-7, 16/00242-2, 19/10269-3, 18/05098-2)

BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; GASULL, ARMENGOL. The local period function for Hamiltonian systems with applications. Journal of Differential Equations, v. 280, p. 590-617, APR 15 2021. (19/10269-3, 16/00242-2, 18/05098-2)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARVALHO, Yagor Romano. Qualitative aspects of piecewise smooth differential systems: regularization, bifurcation, limit cycles and period function.. 2021. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.