Urban-population dynamics in Chengdu: spatiotemporal feedback mechanisms revealed by multi-order adjacency index and time-lagged cross-correlation

As a spatial manifestation of regional development, urban expansion embodies not only the dynamic evolution of land use but also engages in complex spatiotemporal feedback with population mobility. This interplay offers a novel analytical lens for investigating urban system dynamics and deepens mechanistic understanding of urbanization processes. Utilizing long-term time-series data from the Multi-order Adjacency Index (MAI), this study characterizes the spatiotemporal patterns of urban expansion in Chengdu’s central area. Subsequently, a time-lagged cross-correlation model was employed to quantify dynamic interactions between urban growth and population mobility, revealing bidirectional urban-population feedback mechanisms and their spatial heterogeneity—providing a novel analytical perspective for regional planning research. The results reveals distinct spatiotemporal signatures: Spatially, micro-scale expansion has transitioned from inefficient sprawl to intensified peripheral densification. Temporally, the process evolved through three progressive phases—disordered growth, accelerated differentiation, and stratified restructuring—reflecting synergistic development between a compact urban core and a concentric suburban periphery. The urban expansion-population mobility nexus demonstrates a bidirectional driver–response mechanism: Large-scale peripheral construction in outer areas drives subsequent inward migration via lagged effects. Rising population density in the urban core triggers infill development and renewal processes. This study establishes an innovative space–population co-evolution framework, providing theoretical foundations for optimizing urban growth governance and reconciling human–land system relationships.