Andrea Baronchelli and Romualdo Pastor-Satorras J. Stat. Mech. (2009) L11001 doi:10.1088/1742-5468/2009/11/L11001
Andrea Baronchelli and Romualdo Pastor-Satorras
Show affiliationsModels of ordering dynamics allow us to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to social dynamics, are the Voter and Moran processes, usually defined in terms of static or randomly mixed individuals that interact with a neighbor to copy or modify a discrete trait. Here we study the effects of diffusion in Voter/Moran processes by proposing a generalization of ordering dynamics in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place. We show that diffusion dramatically affects the time to reach the homogeneous state, independently of the underlying network's topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength. Our results highlight the crucial role played by mobility in ordering processes and set up a general framework that allows its effect to be studied on a large class of models, with implications in the understanding of evolutionary and social phenomena.
87.23.Ge Dynamics of social systems
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
91D10 Models of societies, social and urban evolution
Issue 11 (November 2009)
Received 18 June 2009, accepted for publication 21 October 2009
Published 4 November 2009
Andrea Baronchelli and Romualdo Pastor-Satorras J. Stat. Mech. (2009) L11001
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