The Self-Organization of Behavioral Rules in Collectives

A set of simple mathematical models based on iterated maps is introduced in this paper. The models describe the self-organization of behavioral rules in collectives of people and animals. The concept of evolutionary stable strategy in biology (ESS, J. Maynard Smith) and the concept of positive feedback in economy (W. Brian Arthur) are used and forwardly developed. The rules dynamics is described phenomenologically, which makes it possible to avoid extremely detailed description of all the elementary interactions between all the individuals in the collective (or population). The models proposed qualitatively predict the variety of verisimilar scenarios for population evolution: asymptotic stable state, regular and chaotic oscillations, 'flourishing and regress' of civilizations, even catastrophic death. Much attention is paid to the history of the questions discussed.