Bifurcations of Degenerated Cycles in Discontinuous Systems

• Grant number: 13/07523-9
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: August 01, 2013
• End date: March 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Kamila da Silva Andrade
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM
• Associated scholarship(s): 14/21259-5 - Typical cycles in piecewise smooth dynamical systems, BE.EP.DR

Abstract

The student will develop research in discontinuous dynamical systems (Filippov Systems), studying bifurcations and con dimension of local and global phenomena occurring in piecewise smooth vector fields. It is about a specially active and important area given several applications in physics an engineering. The research groups in which the supervisor participates has obtained good results combining techniques of several mathematic's areas such as Algebraic Geometry and Symbolic Calculus, further usual methods of Qualitative and Geometric Theory of Dynamical Systems, Singularities Theory and Singular Perturbation Theory.

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)

ANDRADE, KAMILA DA S.; JEFFREY, MIKE R.; MARTINS, RICARDO M.; TEIXEIRA, MARCO A.. Homoclinic Boundary-Saddle Bifurcations in Planar Nonsmooth Vector Fields. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 04, p. 27-pg., 2022-03-30. (18/13481-0, 21/08031-9, 15/06903-8, 12/18780-0, 18/03338-6, 14/21259-5, 13/07523-9)

ANDRADE, K. DA S.; JEFFREY, M. R.; MARTINS, R. M.; TEIXEIRA, M. A.. On the Dulac's problem for piecewise analytic vector fields. Journal of Differential Equations, v. 266, n. 4, p. 2259-2273, FEB 5 2019. (13/07523-9, 18/03338-6, 12/18780-0, 15/06903-8, 14/21259-5)

Academic Publications

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

ANDRADE, Kamila da Silva. Sobre ciclos degenerados em campos vetoriais descontínuos e o problema de Dulac. 2016. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.