Geometric theory of the singularly perturbed differential equations

• Grant number: 13/21947-6
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2014
• End date: January 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Toniol Cardin
• Grantee: Pedro Toniol Cardin
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

In this project the main goal is to study systems of singularly perturbed ordinary differential equations involving multiple different time scales. The study will encompass both the case where the vector field associated to such systems is smooth, as well as the case where the field vector is non-smooth (Filippov kind). The main feature of such systems is the possibility of working at different time scales. We intend to develop a mathematical theory in order to study these systems. The main goal is to build a theory, inspired by the Geometric Singular Perturbation Theory, for systems involving n different time scales, where n is greater than 2. (AU)

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)

CARDIN, PEDRO T.; DE MORAES, JANNE R.; DA SILVA, PAULO R.. Persistence of periodic orbits with sliding or sewing by singular perturbation. Journal of Mathematical Analysis and Applications, v. 423, n. 2, p. 1166-1182, MAR 15 2015. (13/24541-0, 13/21947-6, 10/17956-1)

CARDIN, PEDRO TONIOL; TEIXEIRA, MARCO ANTONIO. Fenichel Theory for Multiple Time Scale Singular Perturbation Problems. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 3, p. 1425-1452, 2017. (13/24541-0, 13/21947-6, 12/18780-0)

CARDIN, PEDRO T.; DA SILVA, PAULO R.; TEIXEIRA, MARCO A.. THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS. QUARTERLY OF APPLIED MATHEMATICS, v. 72, n. 4, p. 673-687, 2014. (13/21947-6, 12/18780-0)