The noisy voter model on complex networks

Abstract

We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity ---variance of the underlying degree distribution--- has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured.

28 pages, 9 figures

References in corpus (15)

• Statistical physics of social dynamics
• Critical phenomena in complex networks
• Thresholds for epidemic spreading in networks
• Voter Models on Heterogeneous Networks
• Generic Absorbing Transition in Coevolution Dynamics
• The entropy of network ensembles
• Conservation laws for the voter model in complex networks
• Percolation and Epidemic Thresholds in Clustered Networks
• Analytical Solution of the Voter Model on Disordered Networks
• Langevin description of critical phenomena with two symmetric absorbing states
• Annealed and Mean-Field formulations of Disease Dynamics on Static and Adaptive Networks
• Return times of random walk on generalized random graphs
• Exact Solution of Ising Model on a Small-World Network
• How does degree heterogeneity affect an order-disorder transition?
• On the effect of heterogeneity in stochastic interacting-particle systems

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