Detecting the interaction between urban elements evolution with population dynamics model

Exploring the evolution of urban elements can improve understanding of the developmental process of city and drive such development into a better direction. However, the non-linearity and complexity of changes in urban elements have brought great challenges to understanding this process. In this paper, we propose a cross-diffusion partial differential equation based on ecological dynamics to simulate the evolutionary process of urban elements from the microscopic viewpoint. The interaction between urban elements is simulated by constructing a non-linear and spatiotemporal change equation, and the main influence between elements is evaluated by the key parameters in the discussed equation. Our model is first experimented to time-series data on population density and housing prices to analyzes the interaction of these two elements in the evolution process. We then extend the model to label data, land cover data, to obtain a quantitative expression of the interaction between different land types in the process of urban land cover change.