Intermittent vector fields: Theoretical aspects and applications.

• Grant number: 22/02819-6
• Support Opportunities: Research Grants - Initial Project
• Start date: February 01, 2023
• End date: January 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Tiago de Carvalho
• 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
• City of the host institution: São José do Rio Preto
• Associated scholarship(s): 25/04699-6 - The 3D cusp-cusp singularity for piecewise smooth vector fields and applications., BP.DR; 24/08665-6 - Qualitative theory of ordinary differential equations and applications to Economy, BP.IC; 24/03715-5 - Existence and properties of discontinuous dynamical systems using differential inclusion, BP.MS; + associated scholarships 24/06060-0 - An introduction to piecewise smooth vector fields and applications, BP.IC; 24/01771-5 - Closing Lemma: a study of the art and the proof of the case C^1, BP.MS; 23/18081-9 - Singular perturbation of codimension-3 singularities of planar piecewise smooth vector fields, BP.DR; 23/05369-4 - An introduction to the qualitative theory of ordinary differential equations, BP.IC; 23/04037-8 - An introduction to the discrete dynamical systems, BP.IC - associated scholarships

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 we quote: 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 smooth vector fields; defining and obtaining properties of sliding vector fields on double tangency manifolds; symbolic dynamics and entropy for piecewise vector fields andsystem dynamics (smooth or piecewise smooth) of singularly perturbed ordinary differential equations.The main researcher obtained his doctorate in 2011 from UNESP, was hired by USP in 2018 and has achieved significant scientific production, guides or supervised undergraduate, master, doctoral and postdoctoral students in lines related to this project, coordinates research projects funded by the main university funding agencies.If it is approved, this project will guide the actions of this main researcher, based in an emerging center, and will financially encourage trips abroad, coming from international collaborators to the State of São Paulo, training of undergraduate and graduate students and production of knowledge of frontier in this research area; this production should be published of scientific articles from journals in the area. (AU)

Scientific publications

(11)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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)

CARVALHO, TIAGO; CUNHA, JACKSON; PEREZ, OTAVIO HENRIQUE. Singular perturbation of a planar saddle-node boundary equilibrium. Journal of Differential Equations, v. 453, p. 36-pg., 2025-11-03. (22/02819-6, 21/10198-9, 19/10269-3, 21/12395-6)

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)

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. 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; 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)

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)