Piecewise smooth vector fields: theory and applications

• Grant number: 21/12395-6
• Support Opportunities: Regular Research Grants
• Start date: February 01, 2022
• End date: 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
• City of the host institution: Ribeirão Preto

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

(12)

(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. Integrable 2D and 3D piecewise smooth vector fields with chaotic behavior and preserving energy or not. PHYSICA D-NONLINEAR PHENOMENA, v. 463, p. 7-pg., 2024-04-19. (19/10269-3, 14/02134-7, 21/12395-6, 22/02819-6)

CARVALHO, TIAGO; NOVAES, DOUGLAS D.; TONON, DURVAL J.. Sliding Mode on Tangential Sets of Filippov Systems. JOURNAL OF NONLINEAR SCIENCE, v. 34, n. 4, p. 18-pg., 2024-08-01. (21/12395-6, 18/13481-0, 19/10269-3, 22/02819-6, 22/09633-5)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO; FREITAS, BRUNO RODRIGUES. Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields. Journal of Differential Equations, v. 440, p. 32-pg., 2025-09-25. (21/12395-6, 19/10269-3, 22/02819-6)

FLORENTINO, MARCO; CARVALHO, TIAGO; CASSIANO, JEFERSON. Some Aspects of Thermodynamic Formalism of Piecewise Smooth Vector Fields. Journal of Dynamics and Differential Equations, v. N/A, p. 23-pg., 2025-06-16. (21/12395-6, 19/10269-3, 22/02819-6)

CARVALHO, TIAGO; ANTUNES, ANDRE DO AMARAL. Symbolic dynamics of planar piecewise smooth vector fields. Journal of Differential Equations, v. 419, p. 25-pg., 2024-11-29. (19/10269-3, 19/10450-0, 21/12395-6, 17/18255-6, 22/02819-6, 17/00883-0)

CARVALHO, TIAGO. Planar quartic-quadratic fold-fold singularity of Filippov systems and its bifurcation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 134, p. 31-pg., 2024-04-17. (21/12395-6, 22/02819-6, 19/10269-3)

CARVALHO, TIAGO; CUNHA, JACKSON; EUZEBIO, RODRIGO; FLORENTINO, MARCO. Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 82, p. 6-pg., 2025-04-01. (21/12395-6, 22/02819-6, 19/10450-0, 19/10269-3)

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)

FLORENTINO, MARCO; CARVALHO, TIAGO. Piecewise smooth vector fields with sliding motion preserving measure. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 57, p. 16-pg., 2025-04-28. (22/02819-6, 19/10269-3, 19/10450-0, 21/12395-6)

ANTUNES, A. A.; CARVALHO, T.; GOMIDE, O. M. L.. Closing Lemma for piecewise smooth vector fields with a recurrent point. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 53, p. 9-pg., 2024-04-09. (19/10450-0, 17/18255-6, 21/12395-6, 19/10269-3, 22/02819-6)

CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO; FREITAS, BRUNO RODRIGUES. Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field. NONLINEAR ANALYSIS-HYBRID SYSTEMS, v. 58, p. 44-pg., 2025-11-01. (19/10269-3, 22/02819-6, 21/12395-6)