The General Urban Distortion Propagation Law: A Novel Dynamic Mathematical Framework for Modeling Shock Propagation and Recovery in Complex Urban Systems

Contemporary cities are increasingly exposed to cascading shocks that propagate through complex and interconnected urban networks, challenging the explanatory power of traditional risk models. This study introduces the General Urban Distortion Propagation Law (GUDPL), an innovative dynamic mathematical framework that integrates functional connectivity, effective distance, time delays, structural vulnerability, recovery dynamics, and irreducible residual effects. The model provides a unified representation of how urban shocks emerge, spread, and attenuate across interconnected systems, and can, in principle, support the identification of vulnerable urban nodes and resilience-oriented planning. To illustrate the operational behavior of the proposed framework, a proof-of-concept simulation based on a stylized cascading power outage scenario is conducted, highlighting delayed propagation, heterogeneous impacts, and recovery processes. GUDPL is adaptable to different crisis types and compatible with time-dependent and real-time modeling contexts, offering a flexible analytical foundation for urban resilience, sustainability, and crisis management research.