Early Warning Signals for Critical Transitions in Sandpile Cellular Automata

Frontiers in Physics. 2022. Vol. 10. No. 839383. Article 839383.

Dmitriev A., Kornilov V., Dmitriev V., Abbas N.

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection of critical transitions precursors in sandpile cellular automata will allow progress significantly in the search for effective early warning signals for critical transitions in complex real systems. The presented paper is devoted to the detection and investigation of such signals based on multifractal analysis of the time series of falls of the cellular automaton cells. We examined cellular automata in square lattice and random graphs using standard and facilitated rules. It has been established that log wavelet leaders cumulant are effective early warning measures of the critical transitions. Common features and differences in the behavior of the log cumulants when cellular automata transit into the self-organized critical state and the self-organized bistability state are also established.

Keywords: early warning signals, self-organized criticality, Sandpile model, Wavelet Leader, self-organized bistability, self-organized criticality, self-organized bistability, Early Warning Signals, Sandpile Cellular Automata

Publication based on the results of: Data analysis and modeling of the structure and dynamics of plasma formations and processes in the solar system responsible for solar-terrestrial communications and processes on Earth (2022)