Predictability of extreme events in a branching diffusion model

Andrei Gabrielov, Vladimir I. Keilis-Borok, Sayaka Olsen, & Ilya Zaliapin

Published 2014, SCEC Contribution #1156

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements --- direct cascading or fragmentation, spatial dynamics, and external driving --- are combined in a classical age-dependent multi-type branching diffusion process with immigration. A complete analytic description of the size- and space-dependent distributions of particles is derived. We then formulate an extreme event prediction problem and determine characteristic patterns of the system behavior as an extreme event approaches. In particlular, our results imply specific premonitory deviations from self-similarity, which have been heuristically observed in real-world and modeled complex systems. Our results suggest a simple universal mechanism of such premonitory patterns and natural framework for their analytic study.

Citation
Gabrielov, A., Keilis-Borok, V. I., Olsen, S., & Zaliapin, I. (2014). Predictability of extreme events in a branching diffusion model. In Gabrielov, A., Keilis-Borok, V. I., Olsen, S., Zaliapin, I., & (Eds.), Extreme Natural Hazards, Disaster Risks and Societal Implications, (, pp. ) , : Cambridge University Press