Discrete Model of Ideological Struggle Accounting for Migration

TL;DR

This paper develops a discrete-time mathematical model of ideological competition that incorporates population migration, media influence, and varying birth rates, providing insights into ideological dynamics across regions and historical contexts.

Contribution

It introduces a novel discrete model accounting for migration, media influence, and different birth rates, extending previous models of ideological competition.

Findings

Complex dynamics of ideological attraction are analyzed.

Migration significantly affects ideological spread.

Historical cases are discussed in light of the model.

Abstract

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.