Against the backdrop of urban–rural integrated development, special ecological function zones, as spatial carriers with significant regional ecological value and rural development functions, are confronted with a striking conflict between ecological conservation and regional advancement. This contradiction is comprehensively reflected in the interactions among land use functions (LUFs) that differ in nature and intensity. Therefore, exploring the trade-off and synergy (TOS) among regional LUFs is not only of great significance for optimizing territorial spatial patterns and advancing rural revitalization but also provides scientific evidence for the differentiated administration of regional land use. Taking 185 townships in the Funiu Mountain area of China as research units, this study constructs a land use assessment system based on the ‘Production–Living–Ecological’ (PLE) framework, utilizing multi-source datasets from 2000 to 2020. Spearman correlation analysis, geographically weighted regression (GWR), and bivariate local spatial autocorrelation methods are employed to examine the spatio-temporal dynamics of LUFs and the spatial non-stationarity of their TOSs. The findings indicate that, throughout the research period, the production function (PF) displayed a fluctuating declining trend, whereas the living function (LF) and ecological function (EF) demonstrated a fluctuating increasing trend. Notably, EF held an absolute dominant position in the overall structure of LUFs. This is highly consistent with the region’s positioning as a special ecological function zone and also a direct reflection of the effectiveness of continuous ecological construction over the past two decades. Spatially, PF is stronger in southern, eastern, and northern low-altitude townships, correlating with higher levels of economic development; LF is concentrated around townships near county centers; and high EF values are clustered in the central and western areas, showing an opposite spatial pattern to PF and LF. A synergistic relationship is observed between PF and LF, while both PF and LF exhibit trade-offs with EF. The TOSs between different function changes demonstrate significant spatial non-stationarity: linear synergy was the primary type for PF-LF, PF-EF, and LF-EF combinations, but each combination exhibited unique spatial characteristics in terms of non-stationarity. Notably, towns identified as having different types of trade-off relationships in the study of spatial non-stationarity are key areas for township spatial governance and optimization. Through the allocation of regional resources and targeted policy tools, the functional relationships can be adjusted and optimized to attain sustainable land use.

Urban vitality varies systematically within the day, yet its time-specific associations with stable built-environment conditions remain insufficiently understood at fine spatial scales. This study examines two-hourly urban vitality in central Zhengzhou, China, using Baidu Heatmap-derived activity intensity and multi-source built-environment data at the parcel scale. Twelve two-hourly MGWR models form the primary analysis, identifying temporal changes in the direction, magnitude, and spatial distribution of local associations. A daily mean MGWR model with the same independent variables serves as an aggregate benchmark. Results show that: (1) vitality exhibited a clear daily pulse while retaining a persistent center–corridor–node structure, with Global Moran’s I ranging from 0.508 to 0.562; (2) the two-hourly MGWR models explained 69.1–81.8% of spatial variation, compared with 39.2–66.1% for OLS, while the daily mean MGWR achieved an R² of 0.791; and (3) relative to the benchmark, the two-hourly coefficient distributions revealed variable-specific association windows, directional transitions, and changing local dispersion across transportation, land-use, and facility variables. These findings establish the added interpretive value of two-hourly analysis, support time-sensitive management, and provide diagnostic evidence on how observed daily activity patterns are distributed in relation to stable urban configurations.