Dynamics, synchronization, and stability in coupled economic models and Colpitts oscillators

• Ano de defesa: 2024
• Autor(a) principal: Molina, Victor Emmanuel Camargo
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Atratores; Ciclos econômicos; Circuito Colpitts; Dinâmica caótica; Expoentes de Lyapunov; Funções de estabilidade mestra; Osciladores eletrônicos; Sistema econômico de Van Der Pol; Sistemas dinâmicos complexos; Teoria do caos
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/59/59135/tde-19112024-121238/

This study investigates the chaotic dynamics and synchronization phenomena in two distinct complex dynamical systems: the Economic Van der Pol System and the Colpitts Circuit. The Economic Van der Pol System, a modified version of the classical Van der Pol oscillator, models economic cycles through interactions between savings, GDP, and foreign capital inflow. It exhibits behaviors ranging from limit cycles to chaos, analyzed using Lyapunov exponents, synchronization states, and the Master Stability Function (MSF). Stable synchronization is observed under specific conditions, with intermittent desynchronization for higher coupling values. These findings enhance understanding of economic stability and business cycle synchronization. The Colpitts Circuit, an electronic oscillator, displays periodic and chaotic behavior under varying parameters. Analysis of coupled Colpitts oscillators reveals synchronization and desynchronization phases governed by the coupling parameter, with insights into intermittent synchronization phenomena and power-law behavior. These findings have significant implications for secure communications and signal processing. By employing advanced methods such as Lyapunov exponents and MSF analysis, this work provides a detailed characterization of chaotic systems, linking nonlinear dynamics with practical applications. The research advances our understanding of highly nonlinear behaviors in economic and electronic systems, emphasizing the intricate balance between stability and chaos. These insights pave the way for future studies on complex networks and the challenges posed by high nonlinearity in chaotic systems.