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

Abstract

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.

Demographic Transformations in the Light of Technological Development: Types of Demographic Reproduction in the Past and in the Future

“…This is, in particular the Near East, where a model has developed with a higher than in Europe but lower than in China population density due to more fertile soils; 4) an arid model, with infertile lands and sparse population, where nomadic animal husbandry was developed. Both models played important roles in history; the nomads were an element that united the World System and was a kind of barbarian periphery (Grinin, Korotayev 2012a, 2018Korotayev, Grinin, Grinin 2021. In addition, we may also speak about the African model, where farming was mainly non-irrigated and manual (Grinin 2011;Korotayev and Khaltourina, 2006;Korotayev et al 2016).…”

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“…Это, в частности, Передний Восток, где за счет более плодородных почв сложилась модель с большим населением, чем в Европе, но с меньшим, чем в Китае; 4) аридная модель, с неплодородными землями и редким населением, где сформировалось кочевое животноводство. Обе модели играли важную роль в истории; кочевники были элементом, который объединял мир-систему, являясь своего рода варварской ее периферией[Grinin, Korotayev 2012;2018;Korotayev et al 2021;2022].Кроме того, можно говорить еще об африканской модели, где земледелие было неполивным и ручным[Гринин 2011], -но эта модель сыграла в историческом процессе небольшую роль; а также о моделях с редким населением и тяжелыми для земледелия условиями, где сформировались хозяйственные типы неземледельческого типа (рыбаки, моряки, воины и т. п.).…”