A Mathematical Model of Influence of the Interaction between Civilization Center and Barbarian Periphery on the World System Development

This article offers an analysis and mathematical modeling of the influence of one of the major factors of the World System macrodynamics throughout most part of its history (since the ‘urban revolution’) – the factor of interaction of civilizations with their barbarian periphery. The proposed mathematical model is intended to describe possible influence of interaction between civilizational core of the World System and its barbarian 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 to identify 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 reason why there was observed not only 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. Achievements of modern barbarology, including the understanding of complexity of the barbarian periphery itself and its heterogeneity are considered. The basic principle of the proposed dynamic model is that sizes, power and level of complexity in realization of external policy functions in nomadic unions (empires) closely correspond to sizes, power and level of political culture and activity of the core states with which nomads constantly had to do (this point has been established in works of the known experts in nomadic studies). Various alternatives are shown in the model, when depending on power and size of one of the two components of the system ‘civilization – barbarian periphery’ studied by us, another one also changes significantly as it has to respond to the challenge properly, or can make less efforts feeling no threat or resistance. This principle is observed throughout the long period of the history of the World System. It is shown that interaction between the civilizational center and barbarian periphery really can explain some characteristic features of the World System dynamics in the 4th millennium BCE – the 2nd millennium CE. The ways of further development of the model are outlined