Intermittent vector fields: theoretical aspects and applications

• Grant number: 22/02819-6
• Support Opportunities: Research Grants - Initial Project
• Duration: February 01, 2023 - 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: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated scholarship(s): 24/08665-6 - Qualitative theory of ordinary differential equations and applications to Economy, BP.IC; 24/06060-0 - An introduction to piecewise smooth vector fields and applications, BP.IC; 24/03715-5 - Existence and properties of discontinuous dynamical systems using differential inclusion, BP.MS; + associated scholarships 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 be interested 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 and system 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)