  Measures of wealth and production have been found to scale superlinearly with
the population of a city. Therefore, it makes economic sense for humans to
congregate together in dense settlements. A recent model of population dynamics
showed that population growth can become superexponential due to the
superlinear scaling of production with population in a city. Here, we
generalize this population dynamics model and demonstrate the existence of
multiple stable equilibrium points, showing how population growth can be
stymied by a poor economic environment. This occurs when the goods and services
produced by the city become less profitable due to a lack of diversification in
the city's economy. Then, relying on critical slowing down signals related to
the stability of an equilibrium point, we present an algorithm for engineering
regime shifts such that a city at a stable equilibrium point may continue to
grow again. The generality of the model and the algorithm used here implies
that the model and algorithm need not be restricted to urban systems; they are
easily applicable to other types of systems where the assumptions used are
valid.
