A NONLINEAR DYNAMICAL MODEL FOR THE DYNASTIC CYCLE

A three-class model of society (farmers, bandits and rulers) is consid ered in order to explain alternation between despotism and anarchy in ancient China. In the absence of authority, the dynamics of farmers an d bandits are governed by the well-known prey-predator interactions. R ulers impose taxes on farmers and punish bandits by execution. Thus, f armers are a sort of renewable resource which is exploited both by ban dits and by rulers. Assuming that the dynamics of rulers is slow compa red with those of farmers and bandits, slow-fast limit cycles can be i dentified through a singular perturbation approach. This provides a po ssible explanation for the accomplishment of an endogenously generated dynastic cycle, i.e. a periodic switching of society between despotis m and anarchy. Moreover, there is numerical evidence for the occurrenc e of a cascade of period-doubling bifurcations leading to chaotic beha viour.