Dynamics, evolution and adaptation on complex networks

Abstract

A myriad of real systems can be described by network theory, like biological and artificial systems. One aspect that permeates most of these systems is how the information diffuses throughout the network. In many cases we see that this occurs in an epidemic regime, a characteristic phase in which the information takes over on the network. We will focus on this phenomenon in brain networks and social contact networks. Epidemic spreading on complex networks is one of the most successful examples of the application of network science. Nevertheless, the majority of studies have so far treated this problem on static networks. However, spreading processes happen in networks with time varying links, or contacts. The spread of information inside the brain takes on in a functional network through temporal links, as well as the spread of disease on social networks. This is related to the structure of the network, which in turn is not fixed with respect to the time scale of the spreading process. Temporal networks provide a framework to assess how spreading processes may be affected by the temporality of contacts, which is more accurate than the static description. In addition, spreading dynamics is also affected by mobility patters of the network structure. This can be modeled by using the metapopulation framework, where multiple particles, information carriers, can occupy a node of the network, which is regarded as a subpopulation of interacting agents. The problem can be treated, then, as a reaction-diffusion system. We will study the relation between metapopulation and temporal networks frameworks, which is still an entirely open question. The study and understanding of epidemic spreading on networks allows us to develop analysis methods and measures in order to build and propose forecasting and controlling measures, either to speed up or slow down the spreading process and also to understand the evolution and consequently adaptation process of the network. This will be applied to different networks of interest, as disease propagation and brain neural networks.