Comparing the vulnerability of different coal industrial symbiosis networks under economic fluctuations

We establish a vulnerability analytical framework of CISN, and illustrate the impact path of economic fluctuation on CISN performance. Based on this, we propose an improved cascading failure model with directed weighted network, and design five network performance indicators (i.e., relative value of cascading failure, average path length, relative value of maximal connected sub-graphs, network efficiency, and structure entropy). Taking three coal eco-industrial parks in China as cases, we simulate and compare the impacts on CISN vulnerability (i.e., equality-based, dependent-based, and nested-based CISNs) of economic fluctuation. The results indicate that the interaction between economic fluctuation and network structure is the key factor in determining system vulnerability. Concerning overall vulnerability, equality-based CISN is highest, dependent-based CISN is next, and nested-based CISN is lowest. Regarding disturbance type, the changes in the five performance indicators of the three types of CISN are more intense under energy price shocks than with declining demand. Moreover, the cascading failure scale of equality-based CISN is greatest with declining demand, while the other two kinds of CISN's is greatest under energy price shocks. Concerning disturbance intensity, equality-based CISN shows initial value sensitivity to economic fluctuation, and nested-based CISN has the strongest tolerances for economic fluctuation. From the network performance perspective, the performance of nested-based CISN is superior to that of dependent-based and equality-based CISNs. Due to longer average path length and lower network efficiency, the failure diffusion trend of equality-based CISN shows the curve of Type-S, and the diffusion rate is smooth and slow. Contrariwise, the initial diffusion rate of dependent-based CISN is the highest, indicating that the loss of system efficiency can somewhat improve the system's anti-risk ability.