Shaw Jonathan D, Restrepo Juan G, Rodríguez Nancy
Department of Applied Mathematics, <a href="https://ror.org/02ttsq026">University of Colorado</a>, Boulder, Colorado 80309, USA.
Phys Rev E. 2024 Nov;110(5-1):054305. doi: 10.1103/PhysRevE.110.054305.
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 nonrent control model; in fact, long-lived 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.
出于理解推动绅士化进程因素的需求，我们引入并分析了两个简单的动态系统，它们对这一现象的三个潜在驱动因素之间的相互作用进行建模。构建的系统基于这样一种假设，即存在三个典型驱动因素：一个会增加社区吸引力的亚群体、社区的吸引力以及社区内房地产的平均价格。第二个模型对第一个模型进行了修改，并实施了一种简单的租金控制方案。对于这两个模型，我们研究了均衡的线性稳定性，并根据系统参数数值确定了振荡解的特征。引入租金控制方案使系统趋于稳定，从某种意义上说，解趋近于均衡的参数范围得到了扩展。然而，租金控制模型产生的振荡时间序列通常比非租金控制模型产生的更加杂乱无章；事实上，在租金控制情况下的某些条件下观察到了长期存在的瞬态混沌。我们的结果表明，即使是城市绅士化的简单模型也可能导致复杂的时间行为。
