Qualitative theory of ordinary differential equations with applications

• Grant number: 22/00595-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2022
• End date: April 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Gabriela Hayashi de Paiva Wong
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project aims to establish the qualitative theory of Ordinary Differential Equations (ODE) and to carry out the study of biological models. That is, we intend to study: the existence, uniqueness, prolongation of solutions and generalized Gronwall inequality, dependence on initial conditions and parameters, Poincaré-Bendixon theory, and homogeneous and non-homogeneous linear systems: stability of linear and perturbed systems and end with the Hartman-Grobman Theorem. Furthermore, it is intended to exemplify this theory through the study of non-linear biological, epidemiological, and/or ecological models.(AU)