Study of polycycles with applications in game theory

• Grant number: 22/14353-1
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2023
• End date: August 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Paulo Henrique Reis Santana
• Supervisor: Armengol Gasull
• 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
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 21/01799-9 - The study of vector fields with applications at game theory, BP.DR

Abstract

Our main goal is to study the polycycles (also known as graphs) of vector fields with two vertical invariant straight lines and two horizontal invariant straight lines. Such family of vector fields is closely linked with Game Theory. More precisely, we aim to study the existence, genericity, stability, cyclicity and bifurcation diagrams of such polycycles. (AU)