Limit cycles Bifurcating from planar centers

• Grant number: 18/04524-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): May 01, 2018
• Effective date (End): April 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ana Cristina de Oliveira Mereu
• Grantee: Ricardo Campanha Almagro
• Host Institution: Centro de Ciências e Tecnologias para a Sustentabilidade (CCTS). Universidade Federal de São Carlos (UFSCAR). Sorocaba , SP, Brazil

Abstract

The objective of this project is to introduce the student in the area of planar dynamic systems by studying the number of limit cycles that bifurcate from a linear center. In the first phase an introductory study will be made on the basic results of the Qualitative Theory of Ordinary Differential Equations, with special emphasis on planar systems. Study of global aspects such as the notion of boundary and attractor sets, Poincaré-Bendixon Theorem and Poincaré's First Return Application in planar systems. In the final phase will be studied the number of limit cycles that bifurcate from a linear center. The Averaging method for detecting periodic orbits will be studied. We will select some mathematical models of natural phenomena involving planar systems and apply this method in order to find limiting bifurcation cycles of centers.