Processos dinâmicos com estados absorventes em redes complexas

• Ano de defesa: 2013
• Autor(a) principal: Ferreira, Ronan Silva
• Orientador(a): Ferreira Junior, Silvio da Costa
• Banca de defesa: Rocha, Márcio Santos , Pinho, Suani Tavares Rubim de , Castro, Tânia Tomé Martins de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Viçosa
• Programa de Pós-Graduação: Doutorado em Física
• Departamento: Física Teórica e Computacional; Preparação e Caracterização de Materiais; Sensores e Dispositivos.
• País: BR
• Palavras-chave em Português: Física estatística e termodinâmica; Transições de fase de não-equilíbrio; Sistemas complexos
• Palavras-chave em Inglês: Statistical physics and thermodynamics; Phase transitions of non-equilibrium; Complex systems
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA
• Link de acesso: http://locus.ufv.br/handle/123456789/960

The complex network theory has been outstanding in the last decades in the study of emergent phenomena from the interaction among agents of a system. Particularly, dynamical processes with absorbing states (that cease their evolution) has been the subject of controversies about mathematical approaches to its description. The prototype for the study of this class is the contact process: the simplest model with these properties, that even though well understood on regular networks, it is challenging our understanding for its description on complex networks. To study the dynamics of the contact process on such networks, we combined the quasistationary method with a master equation approach that we developed. It allowed us to understand the necessary corrections for study it in finite systems, that are the subject of a long scientific debate about the validity of mean-field theories on complex networks. Our studies showed that the heterogeneous mean-field theory describes the contact process on complex networks, in contrast to what was reported in the literature. We verified that this theory provides correct critical exponents, but can not explain corrections for finite sizes on strongly heterogeneous networks. For advance in this debate, we studied the role of structural properties of networks on quasistationary quantities of the contact process and submitted this theory to numerical tests. Furthermore, we have developed a heterogeneous pairs approximation able to explain some points where the heterogeneous mean-field is inaccurate. Finally, we investigated the contact process in several network topologies exploiting particular features of the class of scale-free networks, in which the connectivity distribution among vertices follows a power-law and the class of small-world networks, which has a distribution with an exponential tail. Thus, the dynamics of the contact process was investigated on substrates with different characteristics and the results derived have helped us in the challenge to a better understand of its non-trivial dynamics on complex networks.