Study on Urban Expansion and Population Density Changes Based on the Inverse S-Shaped Function

For decades, the continuous advance of urbanization has led to the continuous expansion of urban land and rapid increase in the total area of cities. The phenomenon of urban land expansion faster than population growth has become widespread. High population density can lead to problems such as traffic congestion and exacerbated air pollution and can hinder sustainable development, affecting the quality of life of urban residents. China is currently in a phase of rapid urbanization, with high urban population density and rapid decline in urban population density. The decrease in urban population density is conducive to promoting sustainable urban development. This study selected 34 cities in China as sample cities and analyzed the spatial expansion and population density changes using land use and population density data from 2000, 2005, 2010, 2015, and 2020 in order to provide reference for controlling population density and promoting sustainable urban development. The conclusions of the study are as follows: In the 34 sample cities, the average urban radius was only 11.61 km in 2000, but reached 17.98 km in 2020, with an annual growth rate of 2.5%. There were significant spatial differences in urban expansion. Beijing and Shanghai, as the most developed cities in China, had urban radii exceeding 40 km, while the less developed cities of Liaoyang and Suzhou had urban radii of only 9 km. Although the population density decreased in most cities, the population density values in first-tier cities in China, such as Tianjin, Beijing, and Shanghai, continued to rise. Cities with loose spatial expansion patterns had faster decreases in population density than compact-type cities. The rate of urban spatial expansion was negatively correlated with changes in population density, with cities that had faster urban spatial expansion also having faster declines in artificial ground density.