Analytical Study of a Stochastic Voter Model Driven by Avalanche-Like Perturbations on a Scale-Free Network

The dynamics of a modified noisy voter model on a time-varying scale-free network is considered. In our model, the changes in the binary state (opinion) of the voters (agents) are caused by the avalanche-like dynamics of the threshold variables (stresses) assigned to them. The temporal evolution of a network is due to the “activity” of the agents, which determines the probability that an agent is connected to its nearest neighbors at a given time. By solving a Fokker–Planck equation for the probability density of the averaged opinion, we show that the behavior of the system is completely determined by the activity of the agents. We also demonstrate that the consensus states are more likely for the system with a large value of the averaged agent degree.