Coupling Functional Heterogeneity Activation and Distance Impedance: A Distance-Decay Model for Urban Population Spatial Interactions

Distance-decay models, which formulate the relationship between interaction intensity and distance, are fundamental to understanding population spatial interactions. However, classical models struggle to capture the non-monotonic distance-decay patterns in city, while statistically driven models lack geographic semantic interpretability for their parameters. Therefore, we propose the Activation-Impedance Decay Model (AIDM). Building upon the distance friction effect, AIDM integrates the driving force of urban functional heterogeneity on spatial interactions. By quantifying this force as an activation process of interaction potential that increases non-linearly with distance, the model accurately reproduces the hump-shaped distribution of spatial interaction. Considering the fractal properties of urban structures and functions, power-law functions are employed to model the non-linear spatial transition gradients of functional heterogeneity and distance friction. Through continuous integration and re-parameterization, AIDM's parameters explicitly quantify the spatial scales of potential activation and distance impedance mechanisms, thereby achieving a quantitative representation and geographical interpretation of the functional heterogeneity range and distance friction intensity. Experimental results across different spatial scales of diverse cities demonstrate that AIDM consistently outperforms baseline models, achieving an AIC reduction of over 29.9%. Correlation analyses with urban functional and structural characteristics further validate the AIDM parameter's geographical semantics. In empirical applications, population spatial accessibility derived from AIDM aligns closely with observed urban vitality distribution. Furthermore, the model effectively differentiates variations in interaction intensities and patterns across distinct functional units. Thus, AIDM provides a highly interpretable analytical tool for uncovering the regularities of complex intra-urban population spatial interactions.