Dynamic processes in complex networks / Processos dinamicos em redes complexas
AUTOR(ES)
David Dobrigkeit Chinellato
DATA DE PUBLICAÇÃO
2007
RESUMO
We study the statistical properties of in²uence networks subjected to external perturbations. We consider networks whose nodes have internal states that can assume the values 0 or 1. The internal states can change depending on the state of the neighboring nodes. We let N1 nodes be frozen in the state 1, N0 be frozen in the state 0 and the remaining N nodes be free to change their internal state. The frozen nodes are interpreted as external perturbations to the sub-network of N free nodes. The system is a generalization of the voter model [25] and can describe a variety of interesting situations, from social systems [26] to physics and genetics. In this thesis, we calculate analytically the equilibrium distribution and the transition probabilities between any two states for arbitrary values of N, N1 and N0 for the case of fully connected networks. Next we generalize the results for the case where N0 and N1 are smaller than 1, representing the weak coupling of the network to an external reservoir. We show that our exact results are excellent approximations for several other topologies, including random, regular lattices, scale-free, star and small world networks, and study the dynamics of these other networks numerically. We then proceed to show that, by appropriately tuning the two parameters from the solution from fully connected networks, N0and N1, to eÿective values when dealing with other, more sophisticated network types, we can easily explain their asymptotic network behaviour. Our model is therefore quite general in applicability, if used consciously
ASSUNTO(S)
voter model deriva genetica modelo de ising redes complexas modelo do eleitor network dynamics dinamica de redes ising model complex networks genetic drift
