Suppressing cascades in a self-organized-critical model with non-contiguous spread of failures

Many complex systems that produce cascading events are thought to be self-organized critical (SOC). So far, models of SOC treat a cascade as a spread strictly between adjacent nodes, while in many real systems, e.g., the power-grid or the brain, this restriction is invalid. Here, we demonstrate for the first time SOC behavior in a model for which the spread is non-contiguous, i.e., not restricted to neighboring nodes. We illustrate our results in a circuit model obeying Kirchhoff’s laws and demonstrate mitigation strategies that avoid large-scale cascades. We found that the following two unconventional strategies break SOC: (1) upgrade lines at random in addition to fixing failures and (2) upgrade a tripped line with one that has a random trip threshold. These results enhance our understanding about the conditions under which SOC can occur and may lead to insights that help avoid catastrophic events in real-world systems.