Opinion evolution and rare events in an open community

There are many multi-stable phenomena in society. To explain these multi-stable phenomena, we have studied opinion evolution in an open community. We focus on probability of transition (or the mean transition time) that the system transfer from one state to another. We suggest a bistable model to provide an interpretation of these phenomena. The quasi-potential method that we used is the most important method to calculate the transition time and it can be used to determine the whole probability density. We study the condition of bistability and then discuss rare events in a multi-stable system. In our model, we find that two parameters, “temperature” and “persuading intensity,” influence the behavior of the system; a suitable “persuading intensity” and low “temperature” make the system more stable. This means that the transition rarely happens. The asymmetric phenomenon caused by “public-opinion” is also discussed.