《Table 3 Assessment indicator system of WSCC and corresponding formulas of catastrophe models》

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《水资源可持续承载力的概念与实证:以中国大陆为例（英文）》

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Note:f（x）is the potential function of the system，that is f（SI）；x is the state variable，that is SI；a、b、c are control variables，they represent domestic water，production water and eco-environmental water，respectively；xa-xc are catastrophe progressi

2.3.1 Analysis of catastrophic traits of water resources system According to Table 1 and the abovementioned WSCC concept，in a given area or a certain inner sector，the ideal values of WI and WCR are 1.Real carrying capacity of water resources higher or lower than theoretical WSCC will lead to either overload or under load of the regional water resources system.Therefore，water resources system has the obvious catastrophic trait and bifurcation（Yao et al.，2013；Li et al.，2013；Sun et al.，2013）.The system changes from one stable state to another when one or more parameters were disturbed to break through the ideal WSCC value or standard of WI by themselves or by outside forces.Finally，system structure and function will change dramatically.Therefore，Catastrophe Theory and the Catastrophe Progression Method were introduced to perform a multi-objective and multi-criteria assessment of the regional WSCC to improve its scientific basis and reliability.