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On the number of limit cycles bifurcating from a linear center

Grant number: 17/21161-3
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): January 01, 2018
Effective date (End): July 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Claudio Aguinaldo Buzzi
Grantee:Matheus de Moraes Trindade
Home 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)