Mathematical Model of Interaction between Civilization Center and Tribal Periphery: An Analysis

This article offers an analysis of a mathematical model of the influence of one of the major factors of the World System’s macrodynamics throughout most of its history (since the ‘urban revolution’) – civiliza-tions’ interaction with their tribal peripheries (described in our previous article). The proposed mathematical model is intended to describe the possible influence of interaction between the civilizational core of the World System and its tribal periphery on the formation of the specific curve of world urbanization dynamics. It simulates completion of the phase transition, the behavior of the system in the attraction basin, and the beginning of the phase transition to the attraction basin of the new attractor. The aim is to identify the role of interaction between the civilizational core and tribal periphery in the formation of an attractor effect during the completion of phase transition – that is, to clarify not only why there a slowdown in growth rates of the main indicators of World System development observed following completion of phase transitions during its development, but why these rates fell, with a subsequent temporary stabilization near some equilibrium level. Achievements of modern studies of tribal peripheries, including our