23 de diciembre de 2008

Analytical solution of the voter model on uncorrelated networks

F. Vazquez, V.  M. Eguíluz, New. J. Phys. 10, 063011 (2008)

We present a mathematical description of the voter model dynamics on uncorrelated networks. When the average degree of the graph is μ ≤ 2 the system reaches complete order exponentially fast. For μ > 2, a finite system falls, before it fully orders, in a quasi-stationary state in which the average density of active links (links between opposite-state nodes) in surviving runs is constant and equal to (μ−2)/3(μ−1) , while an infinitely large system stays ad infinitum in a partially ordered stationary active state. The mean lifetime of the quasistationary state is proportional to the mean time to reach the fully ordered state T, which scales as T ~ (μ−1)μ2N/(μ−2)μ2, where N is the number of nodes of the network, and μ2&lt is the second moment of the degree distribution.We find good agreement between these analytical results and numerical simulations on random networks with various degree distributions.