Solution of voter model dynamics on annealed small-world networks

An annealed version of the Watts-Strogatz network, where long-range connections are randomly chosen at each time step, is considered, where the system remains asymptotically disordered in the thermodynamic limit.

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 tau separates a quasistationary disordered state with coexisting domains from a fully ordered frozen configuration. tau is proportional to the number of nodes in the network, so that the system remains asymptotically disordered in the thermodynamic limit.