Regularization, singular perturbation and Averaging method applied to piecewise smooth vector fields

• Grant number: 12/00481-6
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2012
• End date: March 31, 2014
• 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 studyaspects of the Ordinary Differential Equations Qualitative Theory. Specifically speaking, we will study piecewise smooth vector fieldsand we will apply techniques known as \textit{Regularization}, \textit{Singular Perturbation} and \textit{Averaging Method} in order to obtain qualitative properties of such dynamical 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 many papers can be written and published. (AU)

Scientific publications

(10)

(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)

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)

DE CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO. Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields. Journal of Mathematical Analysis and Applications, v. 418, n. 1, p. 11-30, OCT 1 2014. (10/18190-2, 12/18780-0, 12/00481-6)

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; 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)

DE CARVALHO, TIAGO; TONON, DURVAL JOSE. Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 24, n. 7, JUL 2014. (12/00481-6)

BUZZI, C. A.; DE CARVALHO, T.; DA SILVA, P. R.. Closed poly-trajectories and Poincar, index of non-smooth vector fields on the plane. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, v. 19, n. 2, p. 173-193, APR 2013. (10/18190-2, 12/00481-6, 07/08707-5)

BUZZI, CLAUDIO A.; DE CARVALHO, TIAGO; TEIXEIRA, MARCO A.. Birth of limit cycles bifurcating from a nonsmooth center. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 102, n. 1, p. 36-47, JUL 2014. (07/06896-5, 12/00481-6)

BUZZI, CLAUDIO A.; DE CARVALHO, TIAGO; TEIXEIRA, MARCO A.. On 3-Parameter Families of Piecewise Smooth Vector Fields in the Plane. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 11, n. 4, p. 1402-1424, 2012. (10/18190-2, 07/06896-5, 12/00481-6, 07/08707-5)

BUZZI, CLAUDIO AGUINALDO; DE CARVALHO, TIAGO; TEIXEIRA, MARCO ANTONIO. ON THREE-PARAMETER FAMILIES OF FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 22, n. 12, DEC 2012. (10/18190-2, 07/06896-5, 12/00481-6, 07/08707-5)

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)