Separation time on bounded confidence opinion models

In this paper, we propose a new concept named separation time of the bounded confidence opinion models, the Hegselmann-Krause (HK) model and Deffuant-Weisbuch (DW) model. Different from others who care about the limit states of the opinion dynamics, we try to study the phenomenon among the opinion evolution process. The separation time describes the initial time of the formation of the stable opinion divided groups. We explain why the theoretical limit opinion differences of the agents in the HK dynamics are less than the values in simulations, and give a result better than previous convergence analysis result through the definition of separation time. Then we give one upper bound of the expectation of the separation time of the DW dynamics by stochastic analysis. Finally, we show interesting phenomena through simulations about separation time with agent.