  The works of [Cha-DunAlvInoNieCarFieLaw,Cha-Dun] describe upward sweeps in
populations of city-states and attempt to characterize such phenomenon. The
model proposed in both [TurKor,Tur] describes how the population, state
resources and internal conflict influence each other over time. We show that
one can obtain an upward sweep in the population by altering particular
parameters of the system of differential equations constituting the model given
in [TurKor,Tur]. Moreover, we show that such a system has a unstable critical
point and propose an approach for determining bifurcation points in the
parameter space for the model.
