Generic bifurcations and equivalence relations in piecewise smooth vector fields

• Grant number: 14/18707-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2015
• End date: February 28, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Otavio Henrique Perez
• 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

Abstract

In this project we will study qualitative and geometric aspects about piecewise smooth vector fields (either called discontinuous vector fields or Filippov systems) defined in the plan. The study of such fields has been of great interest in recent years, not only for the beauty and mathematical challenges involved in their analysis, but also by the enormous applicability of discontinuous vector fields in problems of Engineering, Physics, Economics, Biology, Chemistry, and other areas. Our focus will be to study local and global bifurcations of codimension one and two and also some equivalence relations for piecewise smooth vector fields defined in the plan. Classify and characterize generic bifurcations using the phase portrait and the bifurcation diagram of the fields involved and discuss how the two fields can be piecewise smooth equivalent in an equivalence relation and no longer according to another relationship. We will also relate the classical theory of smooth vector fields and the theory of piecewise smooth vector fields. (AU)

Academic Publications

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

PEREZ, Otavio Henrique. Generic bifurcations and equivalence relations in piecewise smooth vector fields. 2017. Master's Dissertation - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.