One of the fundamental problems of contemporary history is to understand the processes governing the rise and fall of polities. The universality of boom-and-bust dynamics associated with the life-cycle of polities tempts to treat the problem mathematically and thus brings it to the framework of cliodynamics. Here we introduce a mathematical model of evolving polity under assumption that its evolution is associated with interactions of certain groups of people, forming the polity and differing by their psycho-ethic characteristics. The model is given in terms of ordinary differential equations and the bust dynamics associated with the rise and fall of polities is modelled as an excitation process, which is the non-linear phenomenon, well known in mathematical biology. We consider the deterministic as well as the stochastic version of the model which we fit to the time-scale of civilization's lifespan. We also expand the model to study interaction between two evolving polities. Investigation is performed using analytical methods as well as numerical integration (i.e. MATLAB simulation).
Keywords: Dynamical system; Ethnogenesis; Excitation; Population dynamics.
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