Mean-field approximation for the Sznajd model in complex networks

Abstract

This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

Diversity and Disorder in the Voter Model with Delays

“…We have found a mechanism for opinion diversity that is fundamentally different from the known ones, such as random opinion changes [2], contrarian agents [1], bounded confidence [3][4][5][6][7][8] or cyclic interactions [13,16,17]. This mechanism is based on the observation that after someone changes their opinion, there might be a period of time right after the change where they are more resistant to a new opinion change.…”

“…Opinion diversity is an ubiquitous trait of human societies, with the results of democratic voting being the largest scale evidence of them (we can cite the results from the 2016 US elections and the ensuing demonstrations as a recent example, showing how fragmented opinions can be in a society). In order to reproduce this diversity behaviour, opinion propagation models that revolve around two opinion states (in favour or against an issue) require the introduction of either interactions that behave like a thermal noise (like contrarian agents [1] and spontaneous opinion changes [2]) with an intensity large enough to be the dominant interaction, or the introduction of a mechanism that freezes the state of the system (like bounded confidence [3][4][5][6][7][8] or the CODA mechanism [9]). On the other hand experiments from psychology suggest that interactions that lead to conformity should be the dominant ones, at least in a local level, as this is the most common outcome of discussion in small groups of people [10][11][12].…”

How Disorder Originates and Grows Inside Order

“…The Ref. [32] studies the model of forming public opinion in a community united through a general network. The master equation describing the time evolution of opinions is presented and solved in MFA.…”

Origin and growth of the disorder within an ordered state of the spatially extended chemical reaction model

“…Так, в [Araújo et al, 2015] изучается модель формирования мнения в обществе, объединенном через общую сеть. Управляющее уравнение, описывающее эволюцию мнения во времени, представлено и решено в MFT, что позволяет охватить наиболее важные особенности относительно стационарного состояния модели.…”

“…Управляющее уравнение, описывающее эволюцию мнения во времени, представлено и решено в MFT, что позволяет охватить наиболее важные особенности относительно стационарного состояния модели. Разработанный в [Araújo et al, 2015] метод может применяться для модели эпидемии и модели «хищник-жертва». В работе [Aguiar et al, 2013] используется MFT для пространственной модели «хозяин-возбудитель», чтобы продемонстрировать возникающие в ней интересные эволюционные свойства.…”