Small-world effects in the majority-vote model

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Paulo R. A. Campos ◽  
Viviane M. de Oliveira ◽  
F. G. Brady Moreira
Keyword(s):  
Majority Vote ◽  
Small World ◽  
Vote Model

Majority-vote model on directed Small-World-Voronoi–Delaunay random lattices

2018 ◽  
Vol 29 (07) ◽  
pp. 1850061
Author(s):  
R. S. C. Brenda ◽  
F. W. S. Lima
Keyword(s):  
Critical Exponents ◽  
Majority Vote ◽  
Small World ◽  
Universality Class ◽  
Two Dimensions ◽  
Critical Properties ◽  
Disordered System ◽  
Vote Model ◽  
Random Lattices ◽  
Second Order Phase Transition

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ([Formula: see text]), as well as the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability [Formula: see text]. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on [Formula: see text] ([Formula: see text]), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.

scholarly journals Three-state majority-vote model on small-world networks

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Bernardo J. Zubillaga ◽  
André L. M. Vilela ◽  
Minggang Wang ◽  
Ruijin Du ◽  
Gaogao Dong ◽  
...  
Keyword(s):  
Social Interactions ◽  
Social Order ◽  
Majority Vote ◽  
Small World ◽  
Opinion Dynamics ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Two Dimensional ◽  
Small World Networks ◽  
Vote Model

AbstractIn this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

scholarly journals MAJORITY-VOTE ON DIRECTED SMALL-WORLD NETWORKS

2007 ◽  
Vol 18 (08) ◽  
pp. 1251-1261 ◽  
Author(s):  
EDINA M. S. LUZ ◽  
F. W. S. LIMA
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Order Parameter ◽  
Majority Vote ◽  
Small World ◽  
Small World Network ◽  
Small World Networks ◽  
Vote Model ◽  
Disorder Phase Transition

On directed small-world networks the majority-vote model with noise is now studied through Monte Carlo simulations. In this model, the order-disorder phase transition of the order parameter is well defined. We calculate the value of the critical noise parameter qc for several values of rewiring probability p of the directed small-world network. The critical exponents β/ν, γ/ν and 1/ν were calculated for several values of p.

Damage spreading in the majority-vote model on small-world networks

2005 ◽  
Vol 348 ◽  
pp. 691-700 ◽  
Author(s):  
Nazareno G.F. Medeiros ◽  
Ana T.C. Silva ◽  
F.G. Brady Moreira
Keyword(s):  
Majority Vote ◽  
Small World ◽  
Small World Networks ◽  
Vote Model ◽  
Damage Spreading

scholarly journals Three-State Majority-Vote Model on Small-World Networks

2021 ◽  
Author(s):  
Bernardo J. Zubillaga ◽  
André L. M. Vilela ◽  
Minggang Wang ◽  
Ruijin Du ◽  
Gaogao Dong ◽  
...  
Keyword(s):  
Social Order ◽  
Majority Vote ◽  
Small World ◽  
Opinion Dynamics ◽  
Square Lattice ◽  
Two Dimensional ◽  
Small World Networks ◽  
Vote Model ◽  
Lattice Network ◽  
Small World Property

Abstract In this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1−q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing the dissensus among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We employ Monte Carlo simulations to investigate the second-order phase transition of the system, and obtain the critical noise qc, as well as the standard critical exponents β/ν, γ/ν, and 1/ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

scholarly journals Tax Evasion and Multi-Agent-Based Model on Various Topologies

2017 ◽  
Vol 01 (02) ◽  
pp. 1730001
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Tax Evasion ◽  
Majority Vote ◽  
Small World ◽  
Stat Phys ◽  
Small World Networks ◽  
Vote Model ◽  
Agent Based ◽  
Multi Agent ◽  
Economics Model

In this work, we use Monte-Carlo simulations to study the control of the fluctuations for tax evasion in the economics model proposed by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coordination. 4 (2009) 1; G. Zaklam, F.W.S. Lima and F. Westerhofd, Physica A 387 (2008) 5857.] via a nonequilibrium model with two states ([Formula: see text]) and a noise [Formula: see text] proposed for [M. J. Oliveira, J. Stat. Phys. 66 (1992) 273] and known as Majority-Vote model (MVM) and Sánchez–López-Rodríguez model on communities of agents or persons on some topologies as directed and undirected Barabási–Albert networks and Erdös–Rényi random graphs, Apollonian networks, directed small-world networks and Stauffer–Hohnisch–Pittnauer networks. The MVM is applied around the noise critical [Formula: see text] to evolve the Zaklan model.

Stochastic resonance in the majority vote model on regular and small-world lattices

2017 ◽  
Vol 31 (29) ◽  
pp. 1750214
Author(s):  
A. Krawiecki
Keyword(s):  
Stochastic Resonance ◽  
Spectral Power ◽  
Majority Vote ◽  
Internal Noise ◽  
Small World ◽  
Time Dependent ◽  
Field Equations ◽  
Vote Model ◽  
Power Amplification ◽  
Mean Field Equations

The majority vote model with two states on regular and small-world networks is considered under the influence of periodic driving. Monte Carlo simulations show that the time-dependent magnetization, playing the role of the output signal, exhibits maximum periodicity at nonzero values of the internal noise parameter [Formula: see text], which is manifested as the occurrence of the maximum of the spectral power amplification; the location of the maximum depends in a nontrivial way on the amplitude and frequency of the periodic driving as well as on the network topology. This indicates the appearance of stochastic resonance in the system as a function of the intensity of the internal noise. Besides, for low frequencies and for certain narrow ranges of the amplitudes of the periodic driving double maxima of the spectral power amplification as a function of [Formula: see text] occur, i.e., stochastic multiresonance appears. The above-mentioned results quantitatively agree with those obtained from numerical simulations of the mean-field equations for the time-dependent magnetization. In contrast, analytic solutions for the spectral power amplification obtained from the latter equations using the linear response approximation deviate significanlty from the numerical results since the effect of the periodic driving on the system is not small even for vanishing amplitude.

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