Identifying the key catastrophic variables of urban social-environmental resilience and early warning signal.

Pursuit of sustainability requires a systematic approach to understand a system's specific dynamics to adapt and enhance from disturbances in social-environmental systems. We developed a systematic resilience assessment of social-environmental systems by connecting catastrophe theory and probability distribution equilibrium. Catastrophe models were used to calculate resilience shifts between slow and fast variables; afterwards, two resilience transition modes ("Less resilient" or "More resilient") were addressed by using probability distribution equilibrium analysis. A tipping point that occurs in "Less resilient" system suggests that the critical resilience transition can be an early warning signal of approaching threshold. Catastrophic shifts were explored between the interacting social-environmental sub-systems of land use and energy (fast variables) and environmental pollution (slow variables), which also identifies the critical factors in maintaining the integrated social-environmental resilience. Furthermore, the early warning signals enable the adaptability of urban systems and their resilience to perturbations, and provide guidelines for urban social-environmental management.