Dynamics and Bifurcations of Differential Systems Which Model Memristive Electronic Circuits

• Grant number: 25/01288-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2025
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: Thayná Machado Catelan
• 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

Application of the qualitative theory and bifurcations of ordinary differential equations 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 existing mathematical models in the literature in order to contribute to understanding the dynamics and bifurcations of memristive circuits. These models will serve as a basis for proposing and studying new circuits 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 of the phase portrait and analysis of bifurcations, varying the control parameters involved in the models to be studied).As well as contributing to the understanding of memristive circuits, the proposed study is intended to enable the student, who has already shown great potential for research in mathematics, to improve and deepen her knowledge, particularly in the area of ordinary differential equations and their applications. Furthermore, the development of this project will provide the scholarship holder with a deeper understanding of the development of research in mathematics, which she has already begun with the IC project, and a maturing in the treatment of scientific literature, thus contributing to her preparation for the development of more advanced research, with the possible entry into a doctorate in the future. (AU)