Mathematical Model of Interaction between Civilization Center and Tribal Periphery: A Description

This article offers a mathematical model describing the influence of one of the major factors of the World System's macrodynamics throughout most of its history (since the ‘urban revolution’) – the interaction between civilizations and their tribal peripheries. The proposed mathematical model is intended to describe the possible influence of the interaction between the World System civilizational core and its tribal periphery on the formation of the specific curve of the world urbanization dynamics. It simulates completion of the phase transition, behavior of the system in the attraction basin and beginning of the phase transition to the attraction basin of the new attractor and is aimed at identifying the role of the factor of interaction between the civilizational core and barbarian periphery in the formation of attractor effect during the completion of phase transition, that is for clarification of the reasons why there was observed not only the slowdown of growth rates of the main indicators of the World System development after completion of phase transitions during its development, but also their falling with the subsequent temporary stabilization near some equilibrium level.