Introduction to the study of limit cycles in planar dynamical systems

• Grant number: 18/26674-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2019
• End date: March 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Toniol Cardin
• Grantee: Murilo de Souza Penteado
• Host Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil

Abstract

The goal of this project is to study nonlinear systems of ordinary differential equations and the important topic about limit cycles. Our focus is on the qualitative theory of nonlinear differential equations. We begin by treating local aspects of the theory with the study of the behavior of the solutions of system near an equilibrium points. After that we pass to global theory with emphasis on the study of isolated periodic solutions (or limit cycles) of system. We mainly focus on the study of results on limit cycles for Liénard systems.