Rigorous mean-field dimensional reduction in heterogeneous network dynamics

• Ano de defesa: 2024
• Autor(a) principal: Bian, Zheng
• 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: Dinâmicas em redes; Grafos aleatórios; Heterogeneous networks; Network dynamics; Random dynamical systems; Random graphs; Redes heterogêneas; Redução de campo médio rigorosa; Rigorous mean-field reduction; Sistemas dinâmicos aleatórios
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55134/tde-30092024-145313/

This thesis presents phenomenological and theoretical studies of a class of heterogeneous random networks, where the network degree distribution follows a power-law, and each node dynamics is a random dynamical system, interacting with neighboring nodes via a random coupling function. We characterize the hub behavior by the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide an explanation for several numerical observations, namely, a scaling relation between system size and frequency of large fluctuations, the system size induced desynchronization, and the Gaussian behavior of the fluctuations. Some fundamental results from random graphs, network dynamics, Markov chains, and random dynamical systems are reviewed and reinterpreted.