The Silk Roads: A mathematical model

This article concerns the problem of mathematical modeling of historical processes. The dynamics of the Silk Roads is described by means of formal spatial equations. Historical data conveys the facts that the location of the trade routes known as the Silk Roads altered profoundly enough from epoch to epoch. These changes arise from a number of causes – population oscillations, economic trends, diseases and warfare – all these factors affected the dynamics of the Silk Roads and sometimes predetermined its rise and demise. Mathematical simulation of the Silk Roads could help to distinguish the most significant factors and to estimate where and when these factors were especially efficient. In this paper we examine the hypothesis considered by Jeremy Bentley. This attitude implies that one of the most important causes of the Silk Road prosperity was the development of large-scale empires. It promoted the trade greatly. On the one hand big empires stimulate exchange of commodities for the rise of supply and demand of bulk and prestige goods, on the other hand they construct roads and related infrastructure that also induces active trade. Finally they bring stability to vast areas; it is of high importance for negotiations as well. The model takes all these aspects into account and demonstrates the oscillations of the Silk Roads activity induced by the rise and demise of large empires such as Roman, Parthian, Mongol empires, Han and Tang dynasties etc. Simulation gives also some additional curious results.