On the number of limit cycles that bifurcate from a linear center

• Grant number: 13/00755-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2013
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Felipe Rocha Felix
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil

Abstract

Introduce the student to the planar dynamic systems by studying the number of limit cycles that bifurcate from a linear center. In a preliminary phase conduct a study and prepare a collection of mathematical models involving ordinary differential equations of first and second orders, solving them analytically and also developing computational experiments. Following will be an introductory study of the basic results of the Qualitative Theory of Ordinary Differential Equations, with special emphasis on planar systems. Study global aspects such as the notion of limit sets and attractors, Poincaré-Bendixon Theorem, and the Poincaré First Return Map in planar systems. In the final phase will be studied the number of limit cycles that bifurcate from a linear center. In preparation, we will see the method integral of Poincaré-Melnikov and the method integral Abelian. We will complete the project showing what is the upper bound of the number of cycles that bifurcate from a center by a linear perturbation of degree n.