The Spatiotemporal Evolution and Development Curve Simulation of China's Urban Agglomerations in the Construction of a Digital Basic Public Service System

The construction of regional basic public service systems often coincides with the formation and development of urban agglomerations, driven by economies of scale that promote cooperative interactions among cities. The digital basic public service system within urban agglomerations exhibits a wave-like climbing trend over time. This study investigates the fundamental principles of this climbing trend, derives a geometric expression through a mathematical model, and establishes a comprehensive evaluation framework integrating digital development and basic public service systems. Using the entropy method and a coupling coordination degree model, the study measures and analyzes the construction levels and spatiotemporal evolution of digital basic public services across urban agglomerations and their constituent cities. A joint strength and threshold model is developed to assess the collaborative intensity of digital basic public services within urban agglomerations, and Matlab simulation is employed to validate the climbing trend of construction levels over time. The findings indicate that the construction level of digital basic public services in China's urban agglomerations is steadily improving, adhering to the climbing trend, though spatial distribution remains uneven, with higher levels in coastal areas and the Yangtze River Economic Belt. The joint strength of digital basic public services among cities within urban agglomerations continues to increase but is constrained by thresholds, with varying breakthrough timings across different urban agglomerations. The wave-like climbing curve of construction levels over time and urban joint development is empirically validated with a strong fit. This research provides quantitative evidence for advancing the integration of digital public service systems within urban agglomerations and offers theoretical and algorithmic guidance to promote the equalization of regional basic public services.