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.

追求可持续性需要一种系统的方法来理解系统的特定动态，以适应和增强社会环境系统的干扰。通过将巨灾理论和概率分布均衡联系起来，我们开发了对社会-环境系统的系统抗灾力评估。突变模型用于计算慢速变量和快速变量之间的弹性变化。之后，通过概率分布均衡分析解决了两种弹性过渡模式（“弹性较小”或“弹性较大”）。“较少弹性”系统中出现的临界点表明，临界弹性转变可能是接近阈值的预警信号。探索了土地利用和能源相互作用的社会环境子系统（快速变量）和环境污染（缓慢变量）之间的灾难性转变，这也确定了维持综合的社会环境弹性的关键因素。此外，预警信号使城市系统具有适应性及其对干扰的适应能力，并为城市社会环境管理提供了指导。