Assessing Spatial Synergies and Trade-Offs Among Production–Living–Ecological Functions for Sustainable Urban Development: A Case Study of the Changchun Metropolitan Area

As a key spatial platform for implementing China’s Northeast Revitalization Strategy, coordinated development of production–living–ecological (PLE) functions in the Changchun Metropolitan Area is crucial for high-quality regional development. This study uses 24 counties (districts) in the metropolitan area as analytical units and develops a quantitative indicator system to evaluate PLE functions. We integrate the entropy-weighted TOPSIS method, social network analysis (SNA), and geographically and temporally weighted regression (GTWR) to examine the spatiotemporal dynamics, spatial correlation networks, and driving mechanisms of the three functions from 2013 to 2023. Temporally, the production function follows a growth–decline–recovery trajectory, the living function increases overall despite fluctuations, and the ecological function strengthens continuously. Overall, the three functions increasingly exhibit coupling and synergy. Spatially, the production function concentrates in core areas and diffuses along major axes. The living function is led by the core and followed by county-level catch-up. The ecological function is higher in the east, relatively stable in the west, and connected by corridors, together forming a multi-center, axis-based synergistic pattern. In the spatial correlation networks, densities of the production and ecological networks remain largely stable, whereas the living network becomes markedly denser. The three networks display distinct topologies and continue to evolve structurally. For driving mechanisms, the GTWR model provides the best fit. Geographic proximity positively contributes to the formation of all three functional networks, while the eight explanatory factors show pronounced spatiotemporal heterogeneity. These findings provide an evidence base for optimizing functional coordination and implementing differentiated spatial governance in metropolitan areas.