Qualitative theory and bifurcations of piecewise smooth vector fields

• Grant number: 14/02134-7
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2014
• End date: April 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Tiago de Carvalho
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

In this research project we will study aspects of the Ordinary Differential Equations Qualitative Theory. Specifically speaking, we will study piecewise smooth vector fields. Among the main challenges encountered when studying such systems include the difficulty in establishing the codimension of singularities. In this project we intend to find the codimension of singularities of piecewise smooth vector fields and also get results on minimal sets and bifurcations of such systems. We emphasize that the line of study proposed here is linked to issues already covered in articles published or submitted for publication by the researcher in recent years. Thus, we expect that during the this project papers can be written and published. (AU)

Scientific publications

(14)

(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.; DE CARVALHO, TIAGO; EUZEBIO, RODRIGO D.. Chaotic planar piecewise smooth vector fields with non-trivial minimal sets. Ergodic Theory and Dynamical Systems, v. 36, n. 2, p. 458-469, APR 2016. (12/00481-6, 14/02134-7, 10/18015-6)

CARVALHO, TIAGO; LLIBRE, JAUME. On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 27, n. 6, JUN 15 2017. (14/02134-7)

BRAGA, DENIS DE CARVALHO; CARVALHO, TIAGO; MELLO, LUIS FERNANDO. Limit cycles bifurcating from discontinuous centres. IMA JOURNAL OF APPLIED MATHEMATICS, v. 82, n. 4, p. 849-863, AUG 2017. (14/02134-7)

CARVALHO, TIAGO; TEIXEIRA, MARCO A.. On piecewise smooth vector fields tangent to nested tori. Journal of Differential Equations, v. 261, n. 7, p. 4008-4029, OCT 5 2016. (12/18780-0, 14/02134-7)

DE CARVALHO, TIAGO; EUZEBIO, RODRIGO DONIZETE; LLIBRE, JAUME; TONON, DURVAL JOSE. DETECTING PERIODIC ORBITS IN SOME 3D CHAOTIC QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 21, n. 1, p. 1-11, JAN 2016. (13/25828-1, 14/02134-7)

CRISTIANO, RONY; CARVALHO, TIAGO; TONON, DURVAL J.; PAGANO, DANIEL J.. Hopf and Homoclinic bifurcations on the sliding vector field of switching systems in R-3: A case study in power electronics. PHYSICA D-NONLINEAR PHENOMENA, v. 347, p. 12-20, MAY 15 2017. (14/02134-7)

CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO; TONON, DURVAL JOSE. Asymptotic stability and bifurcations of 3D piecewise smooth vector fields. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, v. 67, n. 2, APR 2016. (12/18780-0, 14/02134-7, 12/00481-6)

CRISTIANO, RONY; PAGANO, DANIEL J.; CARVALHO, TIAGO; TONON, DURVAL J.. Bifurcations at a degenerate two-fold singularity and crossing limit cycles. Journal of Differential Equations, v. 268, n. 1, p. 115-140, DEC 15 2019. (17/00883-0, 14/02134-7)

BUZZI, CLAUDIO A.; DE CARVALHO, TIAGO; EUZEBIO, RODRIGO D.. Chaotic planar piecewise smooth vector fields with non-trivial minimal sets. Ergodic Theory and Dynamical Systems, v. 36, p. 12-pg., 2016-04-01. (14/02134-7, 12/00481-6, 10/18015-6)

DE CARVALHO, TIAGO; LLIBRE, JAUME; TONON, DURVAL JOSE. Limit cycles of discontinuous piecewise polynomial vector fields. Journal of Mathematical Analysis and Applications, v. 449, n. 1, p. 572-579, MAY 1 2017. (14/02134-7)

BUZZI, CLAUDIO A.; CARVALHO, TIAGO; EUZEBIO, RODRIGO D.. ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS. PUBLICACIONS MATEMATIQUES, v. 62, n. 1, p. 113-131, 2018. (13/24541-0, 14/18508-3, 13/25828-1, 14/02134-7)

DE CARVALHO, TIAGO. On the Closing Lemma for planar piecewise smooth vector fields. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 106, n. 6, p. 1174-1185, DEC 2016. (14/02134-7)

DE CARVALHO, TIAGO; TONON, DURVAL JOSE. Structural stability and normal forms of piecewise smooth vector fields on R-3. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 86, n. 3-4, p. 255-274, 2015. (12/00481-6, 14/02134-7)

CARVALHO, TIAGO; EUZEBIO, RODRIGO D.; TEIXEIRA, MARCO ANTONTO; TONON, DURVAL JOSE. Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field. IMA JOURNAL OF APPLIED MATHEMATICS, v. 82, n. 3, p. 561-578, JUN 2017. (14/18508-3, 13/25828-1, 14/02134-7)