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The noisy voter model on complex networks.

Carro A, Toral R, San Miguel M - Sci Rep (2016)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain.

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.

No MeSH data available.


Related in: MedlinePlus

Fraction of nodes in state 1 on a Barabási-Albert scale-free network.Single realizations. The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
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f1: Fraction of nodes in state 1 on a Barabási-Albert scale-free network.Single realizations. The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .

Mentions: The existence of the referred transition when the system is embedded in a network topology has also been reported in the literature both for the Kirman model4243 and in the context of the noisy voter model44. The above described phenomenology can thus also be observed in different network topologies. As an example, we show in Fig. 1 two realizations of the dynamics for a Barabási-Albert scale-free network corresponding, respectively, to the bimodal [panel a)] and the unimodal regime [panel b)]. A mean-field approach has been proposed in the literature4244, leading to an analytical solution for the critical point which does not depend on any property of the network other than its size, ac = h/N, the transition still being a finite-size effect.


The noisy voter model on complex networks.

Carro A, Toral R, San Miguel M - Sci Rep (2016)

Fraction of nodes in state 1 on a Barabási-Albert scale-free network.Single realizations. The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837380&req=5

f1: Fraction of nodes in state 1 on a Barabási-Albert scale-free network.Single realizations. The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
Mentions: The existence of the referred transition when the system is embedded in a network topology has also been reported in the literature both for the Kirman model4243 and in the context of the noisy voter model44. The above described phenomenology can thus also be observed in different network topologies. As an example, we show in Fig. 1 two realizations of the dynamics for a Barabási-Albert scale-free network corresponding, respectively, to the bimodal [panel a)] and the unimodal regime [panel b)]. A mean-field approach has been proposed in the literature4244, leading to an analytical solution for the critical point which does not depend on any property of the network other than its size, ac = h/N, the transition still being a finite-size effect.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122, Palma de Mallorca, Spain.

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.

No MeSH data available.


Related in: MedlinePlus