Qualitative Theory of Ordinary Differential Equations and applications

• Grant number: 15/24456-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2016
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Raul Lima
• 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 realize the study of biological models. In other words, we intend to study: existence, uniqueness, extension solutions and inequality generalized Gronwall, dependence on the initial conditions and parameters, two-dimensional systems and theory of Poincaré-Bendixon and homogeneous linear and non-homogeneous: stability of linear systems and disturbed and conclude with the theorem of Hartman-Grobman. Also it intended to illustrate this theory by studying non-linear biological and ecological models.