INTRODUCTION TO THE STUDY OF BIFURCATIONS IN UNIDIMENSIONAL AND BIDIMENSIONAL DYNAMICAL SYSTEMS WITH APPLICATIONS

• Grant number: 23/18380-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2024
• End date: July 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: LUCIANO APARECIDO MAGRINI
• Grantee: Guilherme Gonçalves Beletato
• Host Institution: Instituto Federal de Educação, Ciência e Tecnologia de São Paulo (IFSP). Campus São Paulo. São Paulo , SP, Brazil

Abstract

Deterministic and continuous dynamical systems play a fundamental role in describing a broad range of phenomena across various knowledge domains such as Physics, Chemistry, and Biology. In practical applications, it is customary to consider real parameters in the modeling of phenomena in investigation, and it is well-known within the scientific community that this parameter dependence influences the qualitative behavior of the temporal evolution under study. Parameter dependence introduces a significant variety of qualitative changes in the geometry of the flow exhibited by the dynamical system, potentially resulting, for instance, in the creation or extinction of equilibrium points and the observed modification of local stability. These qualitative changes in behavior are known as system bifurcations, and it is crucial to understand them from both applied and theoretical perspectives, investigating and classifying them based on their defining properties.The present research project aims to initiate the scholar into the study of bifurcation theory, focusing on uni and bi-dimensional dynamical systems. This initiative seeks to complement the scholar's initial higher education, preparing them for more advanced and specialized studies in this highly promising research area within Mathematics.