The strength of the minority

In this paper, we focus on the problem of opinion formation by introducing a simple model with a certain community structure. To understand the strength of the community, we took a particular interest in a special problem of how the opinion of a small but cohesive community could persist or even be finally accepted by the majority of the society. Both simulation and analysis has been done in the absence and presence of noise. In the noiseless environment, assuming the population of the community is fixed, if the cohesion of the community reaches a certain level, then the phase transition will occur in the evolution process that the community will never be assimilated even if it can assimilate the other nodes in the network, which depends on the population of the community. On the other hand, in the presence of noise, the process of opinion formation seems more complex that two transition behaviors occur outside and inside the community as the noise level increases. And the outcomes of the evolution may be completely opposite under different noise conditions.