| Abstract: |
| Most complex systems, both natural and artificial, are capable of self-organization to the edge of a phase transition known as the edge of chaos. Examples of such systems include stock markets, online social networks, epidemic spread networks, and many others. The irreversible presence of a complex system on the edge of chaos is characterized by its avalanche-like behavior, which often leads to catastrophic consequences for the system. Therefore, early warning is very important for the system to approach the edge of chaos, which, with sufficient early warning time, will make it possible to take preventive measures to prevent the system from reaching the edge. Real-time early warning systems typically use temporal and/or spatiotemporal early warning measures of self-organization to the edge of chaos. Temporal measures are calculated in a sliding window of a time series corresponding to some dynamic variable, such as the number of reposts on an online social network. Such measures are computationally less complex and more accessible for calculations than spatiotemporal measures, the calculation of which requires information about the interactions between elements of the system in space and time. Recently, it has become increasingly common to hear the assertion that temporary measures are ineffective for the early warning. Moreover, some researchers claim that early warning using such measures is impossible. Therefore, we investigated the effectiveness of temporal and spatiotemporal measures associated with critical slowdown of a complex system as it approaches the edge of chaos. First, we introduce the concept of the effectiveness of an early warning measure in terms of the time of early warning and the number of false warning. Next, we calculate the spatiotemporal and corresponding temporal early warning measures associated with the critical slowdown of the sandpile cellular automaton as a system isomorphic to some real-world systems in the context of systems theory. Finally, we compare the effectiveness of the respective measures. We were able to establish that temporary measures are no less effective than the corresponding spatiotemporal measures. |
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