Improving Bifurcation Diagrams in Chaotic Systems

• Grant number: 24/17134-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Murilo Rodolfo Cândido
• Grantee: Lucca Felipe Gonçalves Anjos
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 23/06076-0 - Averaging based methods for dectecting invariant compact sets, AP.JP

Abstract

This scientific project aims to provide a comprehensive guide for improving the accuracy and visual quality of bifurcation diagrams in chaotic systems. The project focuses on numerical methods and mathematical considerations to obtain more precise and elegant bifurcation diagrams. Key aspects such as transient time, critical slowing down phenomena, and multistability are investigated. Additionally, a solution is proposed to efficiently obtain accurate sketches of bifurcation diagrams by executing the system only once for each parameter value, using the system's state from the previous parameter value as the initial condition. The project utilizes Mathematica software for simulations and analyses.