Article

# Consequence of reputation in the Sznajd consensus model

Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-340 Niterói, RJ, Brazil; Departamento de Física, I3N – Universidade de Aveiro, 3810-193 Aveiro, Portugal; ISB – Universidade Federal do Amazonas, 69460-000 Coari, AM, Brazil
Physics Letters A (Impact Factor: 1.77). 01/2010; DOI: 10.1016/j.physleta.2010.06.036
Source: arXiv

ABSTRACT In this work we study a modified version of the Sznajd sociophysics model. In particular we introduce reputation, a mechanism that limits the capacity of persuasion of the agents. The reputation is introduced as a score which is time-dependent, and its introduction avoid dictatorship (all spins parallel) for a wide range of parameters. The relaxation time follows a log-normal-like distribution. In addition, we show that the usual phase transition also occurs, as in the standard model, and it depends on the initial concentration of individuals following an opinion, occurring at a initial density of up spins greater than 1/2. The transition point is determined by means of a finite-size scaling analysis.

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##### Article: The influence of local majority opinions on the dynamics of the Sznajd model
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ABSTRACT: In this work we study a Sznajd-like opinion dynamics on a square lattice of linear size $L$. For this purpose, we consider that each agent has a convincing power $C$, that is a time-dependent quantity. Each high convincing power group of four agents sharing the same opinion may convince its neighbors to follow the group opinion, which induces an increase of the group's convincing power. In addition, we have considered that a group with a local majority opinion (3 up/1 down spins or 1 up/3 down spins) can persuade the agents neighboring the group with probability $p$, since the group's convincing power is high enough. The two mechanisms (convincing powers and probability $p$) lead to an increase of the competition among the opinions, which avoids dictatorship (full consensus, all spins parallel) for a wide range of model's parameters, and favors the occurrence of democratic states (partial order, the majority of spins pointing in one direction). We have found that the relaxation times of the model follow log-normal distributions, and that the average relaxation time $\tau$ grows with system size as $\tau \sim L^{5/2}$, independent of $p$. We also discuss the occurrence of the usual phase transition of the Sznajd model.
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ABSTRACT: This Letter investigates the finite-time consensus problems of second-order multi-agent systems in the presence of one and multiple leaders under a directed graph. Specifically, we propose two bounded control laws, which are independent of velocity information, to deal with the finite-time consensus tracking problem with one leader and the finite-time containment control problem with multiple leaders, respectively. With the aid of homogeneous theory, some sufficient conditions are established for the achievement of the finite-time tracking control problem of second-order multi-agent systems. Numerical examples are finally provided to illustrate the theoretical results.
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• ##### Article: External activation promoting consensus formation in the opinion model with interest decay
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ABSTRACT: We put forward an opinion model that considers internal decay and external activation or deactivation. Agents may withdraw from the discussion, meanwhile, these inactive agents are likely to be motivated by active neighbors. In addition, external influence from outside circumstances is added to the population. We focus on the majority rule of opinion exchange. Our investigations reveal under the impact of external circumstances, the system evolves to different stable states. One opinion can finally be made dominant when the internal motivation is large sufficiently. However, without external activation, consensus is hardly reached in the system with interest decay.
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