The General Urban Distortion Propagation Law
A Novel Dynamic Mathematical Framework for Modeling Shock Propagation and Recovery in Complex Urban Systems
DOI:
https://doi.org/10.18335/region.v13i1.613Abstract
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.
References
Allen PM (1997) Cities and regions as evolutionary, complex systems. Geographical systems 4: 103–130
Alrasheed H, Alballa N, Al-Turaiki I, Almutlaq F, Alabduljabbar R (2024) City transmission networks: Unraveling disease spread dynamics. ISPRS International Journal of Geo-Information 13
Arieli I, Babichenko Y, Peretz R, Young HP (2020) The speed of innovation diffusion in social networks. Econometrica 88: 569–594
Avni N, Brenner N, Miodownik D, Rosen G (2022) Limited urban citizenship: The case of community councils in East Jerusalem. Urban Geography 43: 546–566
Barabasi AL, P´osfai M (2016) Network Science. Cambridge University Press, Cambridge, UK
Batty M (2005) Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models and Fractals. MIT Press, Cambridge, MA
Batty M (2013) The New Science of Cities. The MIT Press, Cambridge, MA
Berry BJL (1964) Cities as systems within systems of cities. Papers in Regional Science 13: 147–163
Bettencourt LMA, Lobo J, Strumsky D,West GB (2010) Urban scaling and its deviations: Revealing the structure of wealth, innovation and crime across cities. PLoS ONE 5: 13541
Boeing G (2021) Street network models and indicators for every urban area in the world. Geographical Analysis 54: 519–535
Borgatti SP, Brass DJ (2019) Centrality: Concepts and measures. In: Brass DJ, Borgatti SP (eds), Social Networks at Work. Routledge, 9–22
Buldyrev T, Parshani R, Paul G, Eugene S, Havlin S (2010) Catastrophic cascade of failures in interdependent networks. Nature 464
Coaffee J, Lee P (2016) Urban resilience: Planning for risk, crisis and uncertainty. Palgrave, London/New York
Crucitti P, Latora V, Porta S (2006) Centrality measures in spatial networks of urban streets. Physical review. E
Cutter SL, Burton CG, Emrich CT (2010) Disaster resilience indicators for benchmarking baseline conditions. Journal of homeland security and emergency management 7
Dorogovtsev SN, Goltsev AV, Mendes JF (2008) Critical phenomena in complex networks. Reviews of Modern Physics 80: 1275–1335 10 1103 80 1275
Fan C, Jiang X, Mostafavi A (2020) A network percolation-based contagion model of flood propagation and recession in urban road networks. Scientific Reports 10: 13481
Fotheringham AS, O’Kelly ME (1989) Spatial Interaction Models: Formulations and Applications. Kluwer Academic
Haynes KE, Fotheringham AS (1984) Gravity and Spatial Interaction Models. Sage Publication, Beverly Hills, CA
Hsu C, Fan C, Mostafavi A (2021). Limitations of gravity models in predicting fine-scale spatial-temporal urban mobility networks
Huff DL (1963) A probabilistic analysis of shopping center trade areas. Land Economics 39: 81–90
Hägerstrand T (1967) Innovation Diffusion as a Spatial Process. Postscript and translation by Allan Pred. The University of Chicago Press, Chicago and London
Lenormand M, Bassolas A, Ramasco JJ (2016) Systematic comparison of trip distribution laws and models. Journal of Transport Geography 51: 158–169
Linkov I, Trump BD, Trump J, Pescaroli G, Hynes W, Mavrodieva A, Panda A (2022) Resilience stress testing for critical infrastructure. International Journal of Disaster Risk Reduction 82: 103323
Lv Y, Sarker MNI, Firdaus RR (2024) Disaster resilience in climate-vulnerable community context: conceptual analysis. Ecological Indicators 158: 111527
Markolf SA, Chester MV, Eisenberg DA, Iwaniec DM, Davidson CI, Zimmerman R, Chang H (2018) Interdependent infrastructure as linked social, ecological, and technological systems (SETSs) to address lock-in and enhance resilience. Earth’s Future 6: 1638–1659
Masucci AP, Serras J, Johansson A, Batty M (2013) Gravity versus radiation models: On the importance of scale and heterogeneity in commuting flows. Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 88: 022812
Meerow S, Newell JP, Stults M (2016) Defining urban resilience: A review. Landscape and Urban Planning 147: 38–49
Peiris MTOV (2024) Assessment of urban resilience to floods: A spatial planning framework for cities. Sustainability 16: 9117
Pred A (1977) City systems in advanced economies: Past Growth, Present Processes, and Future Development Options. Wiley, London
Rahimi F, Sadeghi-Niaraki A, Ghodousi M, Choi SM (2025) Spatial-temporal modeling of urban resilience and risk to earthquakes. Scientific Reports 15: 8321
Reilly WJ (1931) The law of retail gravitation. Knickerbocker Press
Scott AJ, Storper M (2015) The nature of cities: The scope and limits of urban theory. International journal of urban and regional research 39: 1–15
Sharifi A, Yamagata Y (2017) Towards an integrated approach to urban resilience assessment. APN Science Bulletin 7
Simini F, Gonz´alez MC, Maritan A, Barab´asi AL (2012) A universal model for mobility and migration patterns. Nature 484: 96–100
Tang Y, Piao J, Wang H, Rajib S, Li Y (2025) Predicting cascade failures in interdependent urban infrastructure networks. arXiv preprint: 2503.02890
Taylor MO (2022) Spatial interaction modeling. In: Rey SJ, Franklin RS (eds), Handbook of Spatial Analysis in the Social Sciences. Edward Elgar Publishing, Chapter 12, 208–222,
Tubadji A, Rudkin S (2025) Cultural gravity and redistribution of growth through migration: Cohesion lessons from spatial econometrics and topological data analysis. Papers in Regional Science 104: 100064
Valdez LD, Shekhtman L, Rocca CE, Zhang X, Buldyrev SV, Trunfio PA, Havlin S (2020) Cascading failures in complex networks. Journal of Complex Networks 8: 013
Wang H, Zhao P, Yan XY (2023) Quantifying the overall characteristics of urban mobility considering spatial information. arXiv preprint: 2308.00975
Wang J, Kong X, Xia F, Sun L (2019) Urban human mobility: Data-driven modeling and prediction. ACM SIGKDD explorations newsletter 21: 1–19
Wilson AG (1970) Entropy in Urban and Regional Modelling. Pion Limited, Addison-Wesley Publishing, Boston
Yang Y, Herrera C, Eagle N, Gonz´alez MC (2014) Limits of predictability in commuting flows in the absence of data for calibration. Scientific reports 4: 5662
Yuan X, Geng H, Li Z (2025) Threshold effects of the interaction between urban development and atmospheric pollution. Atmosphere 16: 201
Zenou Y, Hodler R, Raschky P, Amarasinghe A (2018) Spatial diffusion of economic shocks in networks. CEPR Discussion Papers, https://ideas.repec.org/p/cpr/ceprdp/12854.html
Zhang Y, Yang Y, Wei S, Ma Z, Tian M, Sun M, Nie J (2022) Research on spatial structure and resilience of complex urban network: A case study of Jing-Jin-Ji urban agglomeration. Frontiers in Environmental Science 10: 999124
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