From element paradigm to dynamic paradigm: Urban evolution research based on fundamental dynamic models

• Urbanization alternates between steady-state and trend stages, revealing no uniform development path. • Six steady-state thresholds and six interactive evolution stages are identified in this study. • Urbanization-economy dynamics show nonlinear and nonstandard patterns beyond Chenery's model. • Four characteristic states— labor, intellectual, non-, and fluctuating urbanization— are proposed. • A full-process interactive model explains dynamic urban-economic coevolution over time. Against the backdrop of accelerating global urbanization and technological transformation, research on urban evolution based on the element paradigm focuses on static resources and dynamic factors, yet struggles to capture the nonlinear changes inherent in urban evolutionary processes. Studies employing the spatial paradigm can dynamically analyze the evolution of urban spatial structures, but the accuracy of such models is significantly hampered by policy interventions and institutional disruptions. In contrast, the dynamic paradigm, through empirical research, reveals common characteristics in the urban evolution of different nations. However, it still faces limitations in delineating the stages of urbanization processes and explaining the non-standard interactions between urbanization and the economy. To address these gaps, this study synthesizes findings from urban evolution research grounded in the dynamic paradigm. It constructs an analytical framework for urban evolution based on basic laws of fundamental dynamic patterns. Utilizing a mixed-methods approach combining quantitative and qualitative empirical frameworks, the research summarizes the basic laws of urban evolution and establishes a theoretical dynamic model of urban evolution. The study utilizes a database foundation comprising statistical indicators of urbanization rates and GDP per capita for 193 United Nations member states from 1960 to 2022. Employing a classification method based on the steady-state characteristics and trend characteristics of urbanization, the statistical indicators were decomposed into sample groups with shared features for rigorous statistical analysis. The results indicate that the three-stage division of the urbanization process, as summarized by Northam through observation, aligns with the structure of maximum variance between different stages. However, a finer subdivision into six steady-state stage mean intervals better reflects the inherent complexity of urban evolution, leading to the identification of six evolutionary stages in urban evolution. Secondly, a dynamic analysis of all interactive phenomena between the urbanization rate and GDP per capita allows their categorization into four characteristic states of interactive evolution based on two dimensions: the tide of urban and rural migration and economic growth. Finally, by integrating the evolutionary stages of the city with the distinctive states of its interactive development, we establish the urban evolution model that links urbanization and the economy. This provides a solid theoretical foundation and empirical support for the scientific diagnosis of urban evolution quality and the formulate of targeted policies.