  A discrete in time model of ideological competition is formulated taking into
account population migration. The model is based on interactions between global
populations of non-believers and followers of different ideologies. The complex
dynamics of the attracting manifolds is investigated.
  Conversion from one ideology to another by means of (i) mass media influence
and (ii) interpersonal relations is considered. Moreover a different birth rate
is assumed for different ideologies, the rate being assumed to be positive for
the reference population, made of initially non-believers. Ideological
competition can happen in one or several regions in space. In the latter case,
migration of non-believers and adepts is allowed; this leads to an enrichment
of the ideological dynamics. Finally, the current ideological situation in the
Arab countries and China is commented upon from the point of view of the
presently developed mathematical model. The massive forced conversion by
Ottoman Turks in the Balkans is briefly discussed.
