Dynamic Properties of the Voter Model with Stochastic Activation of Links Driven by Avalanche-like Perturbations

In this paper, we study the dynamical modes of the modified noisy voter model. 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 (tensors) assigned to them. The
system under study is considered as a scale-free network in which the nodes represent
elements (agents, voters) and the edges represent possible contacts between the elements.
The structure of the links between voters is not static. Its temporal evolution is due to the
“activity” of the agents. This property determines the probability that an agent is connected
to its nearest neighbors at a given time. Within the model, an agent that is not linked to
neighbors can change its opinion to an opposite one, regardless of the opinions of other agents.
A linked agent can copy the opinion of its neighbor during an avalanche process. Analytically
and numerically, we show that the value of agents’ “activity” completely determines the mode
of opinion dynamics. We derive a critical value of the “activity” at which there is a transition
between two dynamic regimes of the system. In the first case, the system switches between two
consensus states. In the opposite case, the system tends to a state where opposing opinions
coexist and the system-averaged opinion is zero. We show that the analytical approach
describes the behavior of the system qualitatively well.