Dynamical models of some sociological problems

We study a dynamical system modeling an iterative process of choice in a group of agents between two possible results. The studied model is based on the principle of bounded confidence introduced by Hegselmann and Krause. According to this principle, at each step of the process, any agent changes his/her opinion being influenced by agents with close opinions. The resulting dynamical system is nonlinear and discontinuous.
We study both cases of finite and infinite groups of agents. We are mostly interested in the structure and stability of fixed points of the system and in conditions under which any positive trajectory tends to a fixed point.