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Qualitative theory and bifurcations of piecewise smooth vector fields

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)

Articles published in Agência FAPESP Newsletter about the research grant:
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VEICULO: TITULO (DATA)
VEICULO: TITULO (DATA)

Scientific publications (13)
(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)
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. Web of Science Citations: 0.
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. Web of Science Citations: 3.
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. Web of Science Citations: 2.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 8.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 0.
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. Web of Science Citations: 5.
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. Web of Science Citations: 0.
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. Web of Science Citations: 4.
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. Web of Science Citations: 1.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.