  We investigate a class of models for opinion dynamics in a population with
two interacting families of individuals. Each family has an intrinsic mean
field "Voter-like" dynamics which is influenced by interaction with the other
family. The interaction terms describe a cooperative/conformist or
competitive/nonconformist attitude of one family with respect to the other. We
prove chaos propagation, i.e., we show that on any time interval [0,T], as the
size of the system goes to infinity, each individual behaves independently of
the others with transition rates driven by a macroscopic equation. We focus in
particular on models with Lotka-Volterra type interactions, i.e., models with
cooperative vs. competitive families. For these models, although the
microscopic system is driven a.s. to consensus within each family, a periodic
behaviour arises in the macroscopic scale. In order to describe fluctuations
between the limiting periodic orbits, we identify a slow variable in the
microscopic system and, through an averaging principle, we find a diffusion
which describes the macroscopic dynamics of such variable on a larger time
scale.
