Dynamic processes on complex networks

Abstract

In the recent decades, various dynamic process models on complex networks have been built to study the mechanisms by which an opinion, a disease or generally the information spreads in real-world networks. For example, opinion models are developed to illustrate the competition of opinions in a population, and epidemic models are used to describe, e.g. how an epidemic spreads in a social contact network or how information propagates in an online social network. Classic models always assume the homogeneous interactions. For example, the infection rates are the same for all pairs of nodes. However, the infection rates between different pairs of nodes which may depend on e.g. interaction frequencies are usually different , thus heterogeneous. In this thesis, we aim to explore the influence of heterogeneity on dynamic processes especially on the prevalence of an epidemic or opinion. We consider two types of dynamic processes: the Non- Consensus Opinion (NCO) model and the Susceptible-Infected-Susceptible (SIS) model. This thesis is mainly devoted to the latter one. We investigate the heterogeneity in both network topology models, e.g. directed networks, and dynamic process models, such as heterogeneous infection rates.