Piecewise smooth vector fields: theory and applications

• Grant number: 21/12395-6
• Support Opportunities: Regular Research Grants
• Duration: February 01, 2022 - January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Tiago de Carvalho
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this research project we will beinterested in studying new topics related to continuous time Dynamical Systems. We will seek both theoretical results and applications in areas such as: Biology, Engineering and Economics. Among the main results to be studied are: dynamics of evolution models of diseases such as cancer, HIV-AIDS and COVID-19; obtaining minimal sets for piecewise smooth vector fields that have no analogue in the smooth case; defining and obtaining properties of sliding fields in double tangency manifolds; symbolic dynamics and entropy;system dynamics (smooth or piecewise smooth) of singularly perturbed ordinary differential equations. (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)

ANTUNES, ANDRE AMARAL; CARVALHO, TIAGO; VARAO, REGIS. On topological entropy of piecewise smooth vector fields. Journal of Differential Equations, v. 362, p. 22-pg., 2023-03-13. (19/10450-0, 16/22475-9, 19/10269-3, 21/12395-6, 17/18255-6, 17/06463-3)

CARVALHO, TIAGO; FREITAS, BRUNO RODRIGUES. paper The local behavior around switching planes in a mathematical model to chemoimmunotherapy. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 120, p. 13-pg., 2023-06-01. (19/10269-3, 21/12395-6)