title: 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.
authors.affiliation: Departamento de Física Geral, Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, São Paulo, Brazil.
authors.forename: Maycon S
authors.initials: MS
authors.lastname: Araújo
authors.affiliation: Campus Experimental do Litoral Paulista, Universidade Estadual de São Paulo, Praça Infante Dom Henrique s/n, 11330-900 São Vicente, São Paulo, Brazil.
authors.forename: Fabio S
authors.initials: FS
authors.lastname: Vannucchi
authors.affiliation: Departamento de Física Geral, Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, São Paulo, Brazil.
authors.forename: André M
authors.initials: AM
authors.lastname: Timpanaro
authors.affiliation: Departamento de Física Geral, Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, São Paulo, Brazil.
authors.forename: Carmen P C
authors.initials: CP
authors.lastname: Prado