QUALITATIVE THEORY AND BIFURCATIONS OF ORDINARY DIFFERENTIAL EQUATIONS AND APPLICATIONS

• Grant number: 25/00591-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: Carolina Aparecida Manfrin
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 23/06076-0 - Averaging based methods for dectecting invariant compact sets, AP.JP

Abstract

Study of the Qualitative Theory of Ordinary Differential Equations and its applications in mathematical modeling and analysis of natural phenomena, especially those from Physics, Biology and Engineering. The aim is to study the main mathematical models, which will serve as a tool for consolidating knowledge and as a basis for studying new proposed models that do not appear in the literature. The theoretical part will be studied and computational experiments will be carried out using the MAPLE software, covering the numerical solution of the equations and the geometric theory (drawing the phase portrait and studying bifurcations).The aim of the proposed study is to enable the student, who has already shown great potential for mathematical research, to improve and deepen her mathematical knowledge, particularly in the area of Ordinary Differential Equations. Furthermore, the development of this project will provide the scholarship holder with an introduction to the development of mathematical research, maturing in the treatment of scientific literature, and preparing her for the development of more advanced research, with the possible entry into a master's degree and, in the future, a doctorate