Relaxation time as early warning signal of avalanches in self-organizing systems

Avalanches are sudden, destructive, and extremely difficult to forecast natural disasters that can result in numerous fatalities and extensive property damage. Given the immense danger posed by avalanches, there is a significant amount of attention paid to accurately predicting these events. We investigate the predictability of large avalanches in a class of self-organizing systems, which change their internal structure or function in response to external circumstances by manipulating or organizing other elements of the same system. Here, we propose a practical relaxation time to replace a traditional recovery time, and importantly, the relaxation time does not require the removal of part of the resources (perturb state variables) in the environment. This work provides examples of the forest fire model and sandpile model as self-organizing systems in which the relaxation time successfully predicts the onset of large avalanches. Furthermore, the relaxation time can show a consistent with the increasing trend in both oscillatory and nonoscillatory bifurcations, suggesting that the relaxation time is more universal than traditional indirect metrics such as the variance and the lag-1 autocorrelation function. We aim to identify early warning signals before the onset of large avalanches and provide scientific evidence and significant information for managers to formulate mitigation countermeasures and strategic decisions.