Pattern and pseudo-randomness of chaos

• Ano de defesa: 2024
• Autor(a) principal: Alvarenga, João Pedro do Valle
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Aprendizado profundo; Chaos theory; Deep learning; Pseudo-randomness; Pseudoaleatoriedade; Teoria do caos
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/76/76135/tde-22042025-082559/

Dynamical systems are known for their sensitivity to initial conditions, complexity, and seemingly random behavior, which makes understanding their dynamics a challenging task. This research delves into chaotic dynamics by exploring key aspects such as the patterns within chaotic systems and their inherent pseudo-randomness. Specifically, we investigate the dynamics of digits in chaotic orbits, the composition of chaotic maps, the prediction of chaotic time series, and the generation of synthetic chaotic data. This research focuses on discrete chaotic systems, logistic and tent maps, and employs a range of computational approaches, from custom algorithms to advanced deep learning models, to approach these challenges. By developing new methods and applying state-of-the-art deep learning architectures, we aim to uncover hidden structures and enhance the predictive and generative capabilities of chaotic systems. Additionally, this research explores the potential of chaotic systems for applications in cryptography and pseudo-random number generation. The findings offer significant contributions toward a digit perspective on chaotic dynamics, advancing both the theoretical understanding of chaos and its practical applications.