Abstract: The collapse of interdependent networks, as well as similar avalanche phenomena in magnetic, elastic, and ecological systems, is driven by cascading failures. At the critical point, the cascade begins as a critical branching process, where each failing node (element) triggers, on average, the failure of one other node. As nodes continue to fail, the network becomes increasingly fragile and the branching factor grows. If the failure process does not reach extinction during its critical phase, the network undergoes an abrupt collapse. We implement the analogy between this dynamics and a critical ("neutral") birth-death process to derive new analytical results and significantly optimize numerical calculations. In particular, we analyze three key aspects of the dynamics: the probability of collapse, the duration of avalanches, and the length of the cascading plateau phase preceding a collapse. This analysis quantifies how system size and the intensity of the initial triggering event influence these characteristics. Finally, we discuss how similar mechanisms underlie avalanche phenomena in other complex systems, including magnetization dynamics, fracture mechanics, and ecological transitions.
This seminar will also be viewable on Zoom via https://illinois.zoom.us/my/icmt.seminar?pwd=ZU1KbnBLeXZLUmJKc0oyU205cDNDdz09