Updating rules and the voter model (Master thesis defense)

Recent measurements on human activities show that a common characteristic are heavy-tailed interevent time distributions. In this work we claim that these patterns of interaction can be implemented in agent based models by introducing a new update rule by which agents are not updated following a Poisson process as usually. We implement the new update rule in two conceptually different ways: one that is coupled to the states of the agents (endogenous update) and one that is not (exogenous update). The former seems to be of more interest. We use the voter model as the simplest agent based model for competition of two equivalent states and study what is the outcome of the model in terms of order/disorder and in terms of interevent time distributions in different networks (fully connected network, random networks and scale-free networks) and under the different update rules: the standard ones and the new ones proposed here. For the standard update rules the model doesn\'t order and the activity patterns are quite homogeneous with exponential interevent time distributions, while for the new updates the results depend on the way it is implemented. For the exogenous version the model behaves qualitatively the same as with standard update rules, but is able to produce heavy tailed interevent time distributions for some parameters. For the endogenous update rule the macroscopic outcome of the model is different, a coarsening process appears and the system orders; and the interevent time distributions are heavy tailed.