Аннотация: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’) – civilizations’ 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 slow-down 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 understanding of complexity of the tribal periphery itself and its heterogeneity, are considered. The basic principle of the proposed dynamic model is that the size, power and level of complexity in realization of external policy functions in nomadic / ‘barbarian’ unions (empires) closely correspond to the size, power and level of political culture and activity of the core states with which tribal systems constantly had to interact (a point previously established by experts in nomadic studies). Various alternatives are shown in the model. Depending on the power and size of one of the two components of the ‘civilization–tribal periphery’ system, the other component also changes significantly as it has to respond to the challenge properly, or can make less efforts without feeling threat or resistance. This principle is ob-served throughout the long history of the World System. We show that interaction between the civilizational center and tribal periphery can explain some characteristic features of World System dynamics in the 4th millennium BCE – 2nd millennium CE. The patterns of interaction between the periphery and the center of the World System may be useful in understanding current phenomena, such as the migrant crisis of 2015 in Europe.