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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.

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Steady state of the average interface density as a function of the noise parameter a in a linear-logarithmic scale and for three different types of networks: Erdös-Rényi random network, Barabási-Albert scale-free network and dichotomous network.Symbols: Numerical results (averages over 20 networks, 10 realizations per network and 50000 time steps per realization). Solid lines: Analytical results [see equation (21)]. Dashed line: Mean-field pair-approximation (see44). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
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f7: Steady state of the average interface density as a function of the noise parameter a in a linear-logarithmic scale and for three different types of networks: Erdös-Rényi random network, Barabási-Albert scale-free network and dichotomous network.Symbols: Numerical results (averages over 20 networks, 10 realizations per network and 50000 time steps per realization). Solid lines: Analytical results [see equation (21)]. Dashed line: Mean-field pair-approximation (see44). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .

Mentions: This expression can be contrasted with numerical results in Fig. 7, where we present the steady state average interface density 〈ρ〉st as a function of the noise parameter a for different types of networks. The mean-field pair-approximation result derived in44 is also included for comparison.


The noisy voter model on complex networks.

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

Steady state of the average interface density as a function of the noise parameter a in a linear-logarithmic scale and for three different types of networks: Erdös-Rényi random network, Barabási-Albert scale-free network and dichotomous network.Symbols: Numerical results (averages over 20 networks, 10 realizations per network and 50000 time steps per realization). Solid lines: Analytical results [see equation (21)]. Dashed line: Mean-field pair-approximation (see44). 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

f7: Steady state of the average interface density as a function of the noise parameter a in a linear-logarithmic scale and for three different types of networks: Erdös-Rényi random network, Barabási-Albert scale-free network and dichotomous network.Symbols: Numerical results (averages over 20 networks, 10 realizations per network and 50000 time steps per realization). Solid lines: Analytical results [see equation (21)]. Dashed line: Mean-field pair-approximation (see44). The interaction parameter is fixed as h = 1, the system size as N = 2500 and the mean degree as .
Mentions: This expression can be contrasted with numerical results in Fig. 7, where we present the steady state average interface density 〈ρ〉st as a function of the noise parameter a for different types of networks. The mean-field pair-approximation result derived in44 is also included for comparison.

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