We consider the voter model dynamics in random networks with mean- eld approach. We apply a Poisson process in the election of the neighbor whose state will be copied by an active node, which is also chosen according to the same process at each time step. For simpli cation, we consider only two possible Poisson rates distributed in two groups, a fast minority and a slow majority. We nd that, for a critical set of parameters, the system exhibit characteristic patterns, with abrupt alternation between two consensus states in the fast group. After the analysis of Langevin equation, an e ective potential for the fast group is found that models the transition between the state of two alternate consensus and another state where the fast minority oscillates around majority opinion trend.

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2014, Tutor: Marián Boguña