Majority Vote Model on Multiplex Networks

Abstract

wjority vote model on multiplex networks with two independently generted lyers in the form of sleEfree networks is investigted y mens of wonte grlo simultions nd heterogeneous menE(eld pproximtionF sn version of the model under study eh gent with proility 1 − q @0 ≤ q ≤ 1/2A follows the opinions of the mjorities of her neighors within oth lyers if these opinions re identilY otherwiseD she mkes deision rndomlyF he model exhiits seondEorder ferromgneti trnsition s qD the prmeter mesuring the level of internl noiseD is deresedD with ritil exponents depending on the detils of the degree distriutions in the lyersF he ritil vlue qc of the prmeter q evluted in the heterogeneous menE(eld pproximtion shows quntittive greement with tht otined from numeril simultions for rod rnge of prmeters hrterizing the degree distriutions of the lyersF hysX IHFIPTWQGehysoleFIQQFIRQQ egGtopisX opinion formtionD mjority vote modelD multiplex networks

Majority-vote dynamics on multiplex networks with two layers

“…The specific way we formulated the AND-model is to maximize this effect. The KGS model studied in [27], which can be thought of as a variant of AND-model, is also found to display discontinuous transition in 6-RR duplexes, however, both the consensus level and the critical noise parameter are much suppressed compared to the AND-model introduced in this paper ( figure 4(b)). It suggests that the random flipping rule of KGS model in case of no common majority has detrimental effect in attaining global consensus.…”

“…It suggests that the random flipping rule of KGS model in case of no common majority has detrimental effect in attaining global consensus. Note that [27] reported continuous consensus transitions, which we speculate to be due to the large mean degrees of layers considered therein.…”

“…Along with the multiplex OR-and AND-model on k-RR duplexes, shown are the results of majority-vote model on single-layer RR network with degree k (denoted single) and k 2 (denoted double), for the case of k=6. Also shown is the multiplex majority-vote model studied in [27] (denoted KGS).…”

“…It has been studied steadily in the complex networks literature [24][25][26], yet the effect of network multiplexity remains to be fully understood, which is the main aim of this study. A recent paper [27] studied the majority-vote model on multiplex networks, in which a different majority-vote rule than our models was considered, reporting continuous consensus transitions. This paper is organized as follows.…”

“…The OR-and the AND-model results are shown along with the results on single-layer network with degree k (single) and aggregated-layer network with degree k 2 (double). Also shown is the result of KGS model of[27]. Simulations are done with networks of N=10 5 and with MC time steps of t final =2 16 -220 .…”