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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

Interface density on a Barabási-Albert scale-free network.Single realizations (the same realizations shown in Fig. 1). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
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f6: Interface density on a Barabási-Albert scale-free network.Single realizations (the same realizations shown in Fig. 1). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .

Mentions: Let us start the description of our results by emphasizing that individual realizations of the interface density ρ remain always active for any non-zero value of the noise, as it was also the case for the variable n (see Fig. 1). As an example, we show in Fig. 6 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)]. While in the first of them (a < ac) the system fluctuates near full order, with sporadic excursions of different duration and amplitude towards disorder; in the second (a > ac), the system fluctuates around a high level of disorder, with some large excursions towards full order.


The noisy voter model on complex networks.

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

Interface density on a Barabási-Albert scale-free network.Single realizations (the same realizations shown in Fig. 1). 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

f6: Interface density on a Barabási-Albert scale-free network.Single realizations (the same realizations shown in Fig. 1). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
Mentions: Let us start the description of our results by emphasizing that individual realizations of the interface density ρ remain always active for any non-zero value of the noise, as it was also the case for the variable n (see Fig. 1). As an example, we show in Fig. 6 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)]. While in the first of them (a < ac) the system fluctuates near full order, with sporadic excursions of different duration and amplitude towards disorder; in the second (a > ac), the system fluctuates around a high level of disorder, with some large excursions towards full order.

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