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Industrial metabolism and symbiotic coupling has become the base paradigm of green, low-carbon development of coal mining. In the coal industrial symbiosis system (CISS), stability is increasingly fragile because of its unique industrial links and growth environment. Referring to the classic Lotka-Volterra population ecology model, and synthesizing the periodicity and time lag effects of industrial development, two entirely novel and more generalized CISS evolution models with time lag effects in the competitive and reciprocal scenarios are constructed respectively. Moreover, the conditions of CISS stability are proven and discussed through mathematical analysis. Simulation and theorem validation were carried out by taking the largest Chinese coal city, Ordos, as the research object. The main results are as follows. First, the time lag effect is an important factor leading to CISS instability. The shorter the time lag within the CISS, the better the collaboration between industries, and the easier it is that the CISS will achieve a stable ecological balance. Second, when the power of competition dominates, the development of industries within CISS will be inhibited; when the power of cooperation dominates, the evolution of CISS will toward a positive direction. Third, a certain degree of self-inhibition will contribute to the stable development of the industrial symbiosis system. At last, the social service industry not only can boost the industrial diversity within CISS, but also can promote the co-evolution of original and exogenous industries, which plays a positive role in the healthy and stable development of CISS. [ABSTRACT FROM AUTHOR]

In the context of the depth adjustment of the global economy and wild fluctuations in energy prices, the vulnerability issue of the coal mining industrial ecosystem (CMIES) has seriously affected the sustainable development of the regional economy. Comparisons of CMIES health status at a regional level are worthy of being conducted. This not only contributes to understanding a particular coal mining area's situation in regards to CMIES vulnerability, but also helps to discover a meaningful benchmark to learn the experiences in terms of action programmes formulation. In this study, based on the analysis of the vulnerability response mechanism of CMIES to economic fluctuations, an initial indicator system for vulnerability assessment of CMIES was constructed. Ultimately, 14 vulnerability-evaluating indicators and their weights were obtained using rough set attribute reduction. Based on a composite CMIES Vulnerability Index (CVI), the Rough Set-Technique for Order Preference by Similarity to Ideal Solution-Rank-sum Ratio (RS-TOPSIS-RSR) methodology is proposed to conduct the CMIES vulnerability assessment process from an overall perspective. Using this methodology, 33 coal mining areas in China are ranked as well as grouped into three specific groups based on the CVI score. The results demonstrate the feasibility of the proposed method as a valuable tool for decision making and performance evaluation with multiple alternatives and criteria. [ABSTRACT FROM AUTHOR]