A dynamical system model of gentrification: Exploring a simple rent control strategy

TL;DR

This paper develops and analyzes simple dynamical models of gentrification, demonstrating how rent control can stabilize neighborhoods but also induce complex, chaotic behaviors over time.

Contribution

It introduces two dynamical systems modeling gentrification drivers and examines the effects of rent control on system stability and oscillatory behaviors.

Findings

Rent control stabilizes the system by expanding equilibrium regimes.

Rent control can induce disorganized oscillations and transient chaos.

Complex temporal behaviors can emerge even in simple gentrification models.

Abstract

Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the non-rent control model; in fact, long-term transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.