Solution of voter model dynamics on annealed small-world networks

Abstract

An analytical study of the behavior of the voter model on the small-world topology is performed. In order to solve the equations for the dynamics, we consider an annealed version of the Watts-Strogatz (WS) network, where long-range connections are randomly chosen at each time step. The resulting dynamics is as rich as on the original WS network. A temporal scale $τ$ separates a quasi-stationary disordered state with coexisting domains from a fully ordered frozen configuration. $τ$ is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.