Study of limit cycles in piecewise smooth systems on the sphere

• Grant number: 19/00440-7
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date until: September 01, 2019
• End date until: July 26, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Ana Livia Rodero
• Supervisor: Joan Torregrosa I Arus
• 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
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 17/08779-8 - Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds, BP.DR

Abstract

At first, this study aims to classify centers for a special class of piecewise smooth Ordinary Differential Equations defined in the unit sphere. In a second moment, we would like to obtain an upper bound for the number of limit cycles that bifurcate from the center. If this upper bound there exists, we will try to answer the question: how does it depend on the degree of the polynomial perturbations and of the order of perturbation?

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)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. Centers and Limit Cycles of Vector Fields Defined on Invariant Spheres. JOURNAL OF NONLINEAR SCIENCE, v. 31, n. 6, DEC 2021. (17/08779-8, 19/10269-3, 19/00440-7)

BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TEIXEIRA, MARCO A.. Stability conditions for refractive partially integrable piecewise smooth vector fields. PHYSICA D-NONLINEAR PHENOMENA, v. 440, p. 15-pg., 2022-08-08. (18/13481-0, 19/10269-3, 19/00440-7, 17/08779-8)