  We introduce an agent-based model for co-evolving opinion and social
dynamics, under the influence of multiplicative noise. In this model, every
agent is characterized by a position in a social space and a continuous opinion
state variable. Agents' movements are governed by positions and opinions of
other agents and similarly, the opinion dynamics is influenced by agents'
spatial proximity and their opinion similarity. Using numerical simulations and
formal analysis, we study this feedback loop between opinion dynamics and
mobility of agents in a social space. We investigate the behavior of this ABM
in different regimes and explore the influence of various factors on appearance
of emerging phenomena such as group formation and opinion consensus. We study
the empirical distribution and in the limit of infinite number of agents we
derive a corresponding reduced model given by a partial differential equation
(PDE). Finally, using numerical examples we show that a resulting PDE model is
a good approximation of the original ABM.
