A Generalized Population Dynamics Model of a City and an Algorithm for Engineering Regime Shifts

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.