A Generalized Voter Model on Complex Networks |
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Authors: | Casey M Schneider-Mizell and Leonard M Sander |
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Institution: | (1) Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA;(2) Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA |
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Abstract: | We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work
has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult
to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with
two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function
of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state to the other node. Traditional voter model behaviors
can be recovered within the model, as well as the invasion process. We find that on a complete bipartite network, the voter
model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values
of α, exit time is dominated by diffusive drift of the system state, but as the high-degree nodes become more influential, the
exit time becomes dominated by frustration effects dependent on the exact topology of the network. |
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Keywords: | Voter model Complex networks Stochastic processes |
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