The voter model: conservation laws, co-evolution and persistence

The voter model is one of the simplest models that can be implemented in a network. Each agent is located in the nodes of a complex network; the state of a node can only take two values. At each time step one random agent adopts the state of a random neighbor. The simplicity of the model allows us to extract analytical results of its time evolution and to explore the effect on the ordering of different settings. In particular, we will present the effect of network topology in finite size systems as well as in the limit of infinite system sizes, in both directed and undirected networks. We will show conservation laws associated to the dynamics of the voter model, and how to identify the influence of a node in the dynamics. Motivated by recent findings in human dynamics, we will also explore the effect of changing the timing of the update rule in the ordering of the system. Finally we will explore the consequences of the co-evolution of node’s state with the topology.