With the proposal of China's high-quality development strategy, how to promote regional stability and coordinated development based on a deep understanding of the main contradictions and changes in China's society has become the focus of research. High-quality development is a brand-new coordinated development concept, which aims to optimize the economic structure, transform the development model, enhance the development momentum, and take innovation as the primary driving force. How to promote the coordinated development of this region has become a hot issue considered by scholars. The Beijing-Tianjin-Hebei region is the capital economic circle of China, and the purpose of this study is to promote the coordinated and stable development of the region. On this premise, this paper firstly adopts the composite Grey Lotka-Volterra (GLV) model and Fractional GM(1,1) (FGM(1,1)) model to research Water Resources system-Economic System-Industrial System-Technology Innovation System in the Beijing-Tianjin-Hebei region. Secondly, by analyzing the research data, it is found that the relationship between the system is very complex, and the stability calculation results are all below 0. Then, the analysis of the research results shows that there is no obvious coordination among the three regions, and they have not yet reached a state of mutual promotion and stable and coordinated development. Finally, four suggestions are put forward for the coordinated development of the Beijing-Tianjin-Hebei region. This can not only provide direction for the future development of the region but also have reference significance for the development of other regions. Further, accelerate the coordination and unity of all factors of production in China and promote China's development at a deeper and higher level.
Keywords: Beijing-Tianjin-Hebei; Grey Lotka-Volterra; entropy weight method; fractional GM(1,1); stability calculation.