Critical noise of majority-vote model on complex networks

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Hanshuang ChenZhonghuai Hou

Abstract

The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase transition takes place and the topology of the underlying networks is still lacking. In this paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the model's dynamics that can analytically determine the critical noise f(c) in the limit of infinite network size N→∞. The result shows that f(c) depends on the ratio of 〈k〉 to 〈k(3/2)〉, where 〈k〉 and 〈k(3/2)〉 are the average degree and the 3/2 order moment of degree distribution, respectively. Furthermore, we consider the finite-size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise f(c)(N) at which the susceptibility is maximal in finite-size networks. We find that the f(c)-f(c)(N) decays with N in a power-law way and vanishes for N→∞. All the theoretical results are confirmed by performing the extensive Monte Carlo simulatio...Continue Reading

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Citations

Feb 27, 2018·Physical Review Letters·M Carmen MiguelRomualdo Pastor-Satorras
Jul 18, 2018·Physical Review. E·Hanshuang Chen, Guofeng Li
Sep 3, 2017·Chaos·Hanshuang ChenJürgen Kurths
Sep 11, 2019·Physical Review. E·C E Fernández NoaC E Fiore
Jan 20, 2018·Physical Review. E·Pedro E HarunariC E Fiore
May 17, 2017·Physical Review. E·Hanshuang ChenJürgen Kurths
Jan 20, 2018·Physical Review. E·Agata Fronczak, Piotr Fronczak
Jun 9, 2018·Scientific Reports·André L M Vilela, H Eugene Stanley
Nov 28, 2019·Physical Review. E·M-Carmen Miguel, Romualdo Pastor-Satorras
Jan 21, 2021·Physical Review. E·Hanshuang ChenGinestra Bianconi
Mar 20, 2021·Physical Review. E·Minsuk Kim, Soon-Hyung Yook
Apr 18, 2021·Physical Review. E·Jesus M Encinas, C E Fiore

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