On the number of limit cycles bifurcating from a linear center

• Grant number: 17/21161-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2018
• End date: July 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Matheus de Moraes Trindade
• 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
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

Introduce the student to planar dynamic systems by studying the number of limit cycles bifurcating from a linear center. In a preliminary phase develop a theoretical study and preparation of a collection of mathematical models involving ordinary differential equations of first and second orders of special types, solving them analytically and also developing computational experiments. 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 limit sets and attractors, Poincaré-Bendixon's Theorem and Poincaré's First Return Application in planar systems. In the final phase the number of limit cycles bifurcating from a linear center will be studied. As a preparation we will see the integral method of Poincaré-Melnikov and the method of the abelian integral. We conclude the project by showing which is the upper bound of the number of limit cycles that bifurcate from a linear center by a degree n perturbation. (AU)