  Following the ideas of L.N.Gumilev, we introduce the mathematical model of
ethnogenesis which describes the dynamics of subgroups in the developing polity
in terms of ordinary differential equations. The bust dynamics associated with
the rise and fall of civilisations is modelled as an excitation process, which
is the non-linear phenomenon, well known in mathematical biology. We consider
deterministic as well as the stochastic version of the model. We also expand
the model to study the interaction between two polities undergoing
ethnogenesis. Investigation is performed using analytical methods as well as
numerical integration (i.e. MATLAB simulation).
