Qualitative Theory and Bifurcations of Dynamical Systems and Applications in the Study o Memristive Electronic Circuits

• Grant number: 25/00457-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2025
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: João Victor Fernandes Silva
• 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 the mathematical modeling and analysis of electrical circuits involving the fundamental components of electronics: resistors, capacitors, inductors and memristors. The aim is to study the main mathematical models of these circuits, 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 MAPLE and MATHEMATICA software, covering the numerical solution of the equations and the geometric theory (drawing the phase portrait and analyzing bifurcations, varying the control parameters involved in the models to be studied). The aim of the proposed study is to enable the student, who has already demonstrated excellent potential for research in Mathematics, to improve and deepen his knowledge, particularly in the area of Ordinary Differential Equations and their applications.