Analytical solution of the voter model on uncorrelated networks

FEDERICO VAZQUEZ; VICTOR M. EGUILUZ

NEW JOURNAL OF PHYSICS

IOP PUBLISHING LTD

Año: 2008 vol. 10 p. 63011 - 63011

1367-2630

We present a mathematical description of the voter model dynamicson 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 quasi-stationary state is proportional to the mean time to reach the fully ordered state T,which scales as T ∼ (μ−1)μ^2 N/(μ−2)μ_2, where N is the number of nodes of the network and μ_2 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.