Characterization of Parameter Space for Nonlinear Systems

• Grant number: 24/05176-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Duration: September 01, 2024 - February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Iberê Luiz Caldas
• Grantee: Iberê Luiz Caldas
• Visiting researcher: Silvio Luiz Thomaz de Souza
• Visiting researcher institution: Campus Divinópolis/Cd/Ufsj, Brazil
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/03211-6 - Non linear dynamics, AP.TEM

Abstract

We will investigate the nonlinear dynamics, in a two-dimensional space of control parameters, of systems exhibiting quasi-periodic behaviors. Our main objective is to meticulously identify and characterize the transition scenarios to chaos involving quasi-periodicity (torus) and strange nonchaotic attractors. Additionally, we intend to examine the variations of periodic windows, including resonance tongues and shrimps, within the parameter space induced by external perturbations. A comprehensive understanding of these variations serves as a crucial tool in the development of control strategies to suppress chaotic behaviors. In our investigation, we will consider auto-parametric oscillators and electrical circuits with memristors. We will develop computational algorithms using the C programming language to investigate the systems under consideration. We will utilize the Linux operating system as a working platform and its applications in which the algorithms will be developed and the results of numerical simulations analyzed. (AU)