Majority-vote dynamics on multiplex networks with two layers

Abstract

Majority-vote model is a much-studied model for social opinion dynamics of two competing opinions. With the recent appreciation that our social network comprises a variety of different 'layers' forming a multiplex network, a natural question arises on how such multiplex interactions affect the social opinion dynamics and consensus formation. Here, the majority-vote processes will be studied on multiplex networks with two layers to understand the effect of multiplexity on opinion dynamics. We will discuss how global consensus is reached by different types of voters: AND-and OR-rule voters on multiplex-network and voters on single-network system. The AND-model reaches the largest consensus below the critical noise parameter q c . It needs, however, much longer time to reach consensus than other models. In the vicinity of the transition point, the consensus collapses abruptly. The OR-model attains smaller level of consensus than the AND-rule but reaches the consensus more quickly. Its consensus transition is continuous. The numerical simulation results are supported qualitatively by analytical calculations based on the approximate master equation.

Pair approximation for the $q$-voter model with independence on multiplex networks

“…Such predictions can be obtained, e.g., by extending the general formulation of the heterogeneous PA for systems on monoplex networks [24,25] to the case of MNs, as it was done in Ref. [40] for the majority-vote model on MNs. It should be mentioned that also the cases of the q-voter model with independence on MNs with partial overlap and with correlations between degrees of nodes within different layers can be relatively easily studied in the framework of the above-mentioned extension.…”

“…Interacting systems on MNs exhibit rich variety of collective behavior and critical phenomena. For example, percolation transition [29,30], cascading failures [31], threshold cascades [32,33], diffusion processes [34,35], epidemic spreading [36] and phase transitions in the equilibrium Ising model [37,38] and related Ashkin-Teller model [39] and in a non-equilibrium majority vote model [40] were studied on MNs. Also the q-voter model with independence [16] and the q-neighbor Ising model [22] were studied on MNs with layers in the form of complete graphs.…”

A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks

“…In order to check the validity of our analytical considerations (in a similar way to, e.g., [ 12 , 17 , 24 , 33 , 34 ]), we performed Monte-Carlo simulations for selected parameters: ( Figure A1 a: , Figure A1 b: ) and ( Figure A2 a: , Figure A2 b: ). Each simulation starts either with a fully ordered (all voters with spins up, red points in Figure A1 and Figure A2 ) or a disordered (spins set randomly, blue points).…”

“…In the last decade, multiplex networks [ 19 ] were proposed as an elegant tool to model such aspects of activity and, without any doubt, they have become one of the most active areas of recent network research mainly due to the fact that many real-world systems possess layers in a natural way [ 20 ]. A lot of attention has also been devoted to the analysis of various dynamics on multiplex networks, including diffusion processes [ 21 , 22 ], epidemic spreading [ 23 ], majority-vote [ 24 ], and voter dynamics [ 25 , 26 ]. The q -voter model examined on a duplex (i.e., consisting of two levels) networks as well as on an arbitrary number L of layers [ 12 ] brings interesting results: the value of q for which the transition changes its character from continuous to discontinuous moves from observed for a monoplex (i.e., ) to for a duplex.…”

Dynamics of opinion formation on complex social networks

“…As pointed out in Chapter 2, existing studies on opinion dynamics have largely been based on isolated single networks while many modern real-life social networks have witnessed the concurrent activeness of their members on various social networks. Such observations have motivated recent studies on various social dynamics in multiplex networks [142][143][144].…”