Mean-field theory for the ordering transition in the majority-vote model on multiplex networks with two independently generated layers in the form of scale-free networks is presented. In this model two-state agents (spins) located in the nodes update their states according to the opinions of the majorities of their neighbors in both layers with certain probability related to the degree of the internal noise. If the opinions of the majorities of the agent's neighbors in both layers coincide the agent adjusts her opinion to them with higher probability; otherwise, she acts independently and makes the decision for or against randomly, with equal probability. An interesting property of the model is that within the mean-field approach the nodes with odd and even number of neighbors within each layer should be taken into account in a different way. The critical values of the internal noise evaluated theoretically for the layers with different degree distributions agree quantitatively with those obtained from Monte Carlo simulations.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/32406 must be provided.

1. Monte Carlo studies of the p-spin models on complex scale-free hypernetworks
2. Structural stochastic multiresonance in systems with a structure of hierarchical networks
3. Microscopic spin model for the stock market with attractor bubbling on scale-free networks