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 \u201cVoter-like\u201d dynamics which is influenced by interaction with the other family. The interaction terms describe a\u00a0 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.<\/p>\n","protected":false},"excerpt":{"rendered":"
We investigate a class of models for opinion dynamics in a population with two interacting families of individuals. Each family…<\/p>\n