Bifurcation of Limit Cycles from Polycycles in Dynamical Systems

• Grant number: 24/21067-0
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: March 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Tiago Miguel Pires de Abreu
• Supervisor: Jordi Villadelprat
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Universitat Autònoma de Barcelona (UAB), Spain
• Associated to the scholarship: 22/07654-5 - Invariant sets and chaotic behavior in piecewise smooth dynamical systems on compact manifolds of low dimension, BP.DR

Abstract

This research project investigates bifurcations in planar dynamical systems, with a focus on the bifurcation of limit cycles from polycycles. The study is structured around three problems: (1) analyzing time delay near saddle-node bifurcations; (2) exploring bifurcations of critical periodic orbits in the Loud family of quadratic centers; and (3) examining the formation of limit cycles in a particular family of Filippov systems. All three problems address issues closely related to Hilbert's 16th problem and its various weak versions.