Spatial Historical Dynamics: Mathematical Approach.
Artemy S. Malkov, Keldysh Institute of Applied Mathematics RAS, Russia

The paper concerns some possibilities of mathematical modeling of spatial historical dynamics. Using spatial differential equations we construct a system of basic models, which represent different aspects of historical dynamics – demography, economics, politics, warfare etc.
The models were examined using historical data.

The work is supported by RFBR (projects No 06-06-80459; 07-06-00314; 07-01-00618) and RFH (No 05-03-03188)

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Spatial Model of the World System Urban Dynamics
Andrew V. Korotaev

We propose a compact macromodel designed to describe mathematically some basic features of spatial urban dynamics of the World System. As one can see in the dynamic map produced by our OPENHISTORY.NET system, the structure of the curve of the World System urban population growth turns out to be rather complex.

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Spatial Distribution of “imperiogenesis”: Why do Large States Tend to Arise on the Nomadic Pastoralist/settled Agriculturalist Frontiers?
Peter Turchin, University of Connecticut, USA

There is a striking macrohistorical pattern: largest territorial polities tend to arise at interfaces between settled and nomadic societies. This is not a strict “law,” but a strong statistical correlation. An example of this pattern is the recurrent state formation in East Asia. According to one enumeration, China has been unified 14 times throughout its history, and on all but one occasion the unification proceeded from north (and most frequently, Northwest) towards south. At the same time, there was a series of nomadic imperial confederations arising on the steppe side of the Inner Asian nomad/settled frontier. I will present a simple model providing a potential explanation for this empirical pattern.