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

Our Yearbook ‘History and Mathematics’ has already celebrated its 10th anniversary
and has confidently entered its second decade. The common feature of all our Yearbooks,
including the present volume, is the usage of formal methods and social studies methods in
their synthesis to analyze different historical phenomena.
The present Yearbook (which is the seventh in the series) is subtitled ‘Big History
Aspects’. This issue is devoted to the problems of evolutionary development of the world.
In no way will it be a digression from the direction which we have initially defined for our
Yearbook, but just an extension of the scope of the research. The matter is that there are
two kinds of history: the history of nature (or more exactly the Universe and the Earth) and
the history of humans and mankind. It is not surprising that the idea of historicism penetrated
almost every scientific field. At the same time the search for common foundations of
this endless in its diversity world has intensified. One of the directions of this interdisciplinary
search for the unity of the world in its diversity is Universal Evolutionism (Big History).
Mathematical and formal methods help to understand much deeply both natural and
human history.