Redes acopladas: Estrutura e dinâmica

Complex network theory has become very popular because of its interdisciplinarity, conceptual simplicity and wide applicability to model real systems. Although fast growing, there is a number of problems which have not been addressed by using complex networks. For example, few efforts have been directed to systems involving coupling and interaction between different complex networks. In the following monography, we present two fundamental contributions in the study of such systems. The first consists in a model which describes the interaction dynamics between a mass pattern evolving in a regular network with a complex network, which are expected to control the pattern evolution. As soon as a complex network node is activated by the regular network, it requests help from its topological neighbours and activates them. The activation is triggered when the mass concentration overcomes a threshold in the node position and consists in liberating an opposite diffusion intended to eliminate the original pattern. The dynamics is completely related to the structure of the control network. The existence of hubs in the Barabási-Albert model plays a fundamental role to accelerate the opposite mass generation. Conversely, the uniform distribution of neighbours in the Erdös-Rényi network provided an increase in the efficiency when several focuses of the original pattern were distributed in the regular network. The second contribution consists in a model based on interactions between two species (predator and prey) provided by sensitive fields which depends of the Euclidean distance between two agents and on their respective types. Spatio-temporal patterns emerge in the system which are directly related to the attraction intensity between same species agents. To understand the dynamics evolution and quantify the information transfer through different clusters, we built two complex networks where the nodes represent the agents. In the first network, the edge weight is given by the Euclidean distance between two agents and, in the second network, by the amount of time two agents become close one another. By following a merging process, another network is obtained whose nodes correspond to spatial groups defined by a weight thresholding process in the first network. Some configurations favor the preys survival, while predators efficiency are improved by other ones.