Investigating vulnerability of ecological industrial symbiosis network based on automatic control theory

System fluctuations of eco-industrial symbiosis network (EISN) organization due to disturbance are very similar to the controller adjustment in the automatic control theory. Thus, a methodology is proposed in this study to assess the vulnerability of EISN based on the automatic control theory. The results show that the regulator plays a key role to enhance the resilience of the network system to vulnerability. Therefore, it is imperative to strengthen the real-time regulation and control of EISN so that the system stability is improved. In order to further explore the impact of various regulations on the system vulnerability, the influence of system stability is simulated by means of proportional, differential, and integral control. A case study with Guigang eco-industrial park (EIP) was undertaken to test this model. The results showed that when the system was disturbed at different positions, the key nodes which had great influence on system vulnerability could be selected according to the magnitude of simulation curve. By changing the ratio coefficient of proportional, differential, and integral units to adjust the ecological chain network, the system's resilience to vulnerability can be enhanced. Firstly, if basic conditions of EISN organization remain unchanged, the integral control of the policy support and infrastructure sharing should be strengthened. Secondly, the differential regulation should be improved continuously for the technological innovation capability of key node enterprises. Finally, the key chain filling projects should be introduced for proportional control so that the chain network design can be optimized from the source.