The coupling and coordination of "production-living-ecological" functions in shrinking cities in the Yellow River Basin

On the basis of the fifth, sixth and seventh national population census data, we identify the shrinking cities in the Yellow River Basin and measure their shrinkage intensity. The multi-index comprehensive evaluation method and the coupling coordination model were used to analyze the size of the "production-living-ecological" functions and the coupling coordination scheduling of shrinking cities in 2010, 2015 and 2020. We also use the random forest model to explore its key influencing factors. The results show that among the 90 prefecture-level cities（stages and leagues） in the Yellow River Basin, there are 27 continuous contracting cities, 9 stage contracting cities and 29 potential contracting cities. The phenomenon of urban contraction is significant. During the study period, the production and living functions of the shrinking cities in the Basin were on the rise as a whole, and the level of "production-living-ecological" functions in different regions was significantly different. The coupling coordination degree of the shrinking cities' "production-living-ecological" functions was characterized by the development from barely coordinated to primary coordinated development. The coordination degree of the middle and lower reaches was better than that of the upper reaches. The development of economic society and the improvement of people's living standards contributed to the coupling and coordinated development of the "production-living-ecological" functions.