Effective precursors for self-organization of complex systems into a critical state based on dynamic series data

Abstract

Many different precursors are known, but not all of which are effective, i.e., giving enough time to take preventive measures and with a minimum number of false early warning signals. The study aims to select and study effective early warning measures from a set of measures directly related to critical slowing down as well as to the change in the structure of the reconstructed phase space in the neighborhood of the critical transition point of sand cellular automata. We obtained a dynamical series of the number of unstable nodes in automata with stochastic and deterministic vertex collapse rules, with different topological graph structure and probabilistic distribution law for pumping of automata. For these dynamical series we computed windowed early warning measures. We formulated the notion of an effective measure as the measure that has the smallest number of false signals and the longest early warning time among the set of early warning measures. We found that regardless of the rules, topological structure of graphs, and probabilistic distribution law for pumping of automata, the effective early warning measures are the embedding dimension, correlation dimension, and approximation entropy estimated using the false nearest neighbors algorithm. The variance has the smallest early warning time, and the largest Lyapunov exponent has the greatest number of false early warning signals. Autocorrelation at lag-1 and Welch’s estimate for the scaling exponent of power spectral density cannot be used as early warning measures for critical transitions in the automata. The efficiency definition we introduced can be used to search for and investigate new early warning measures. Embedding dimension, correlation dimension and approximation entropy can be used as effective real-time early warning measures for critical transitions in real-world systems isomorphic to sand cellular automata such as microblogging social network and stock exchange.

Twitter Self-Organization to the Edge of a Phase Transition: Discrete-Time Model and Effective Early Warning Signals in Phase Space

“…Teir Efectiveness. We study the most efective EWMs for SCA (see the paper [28]), which are both directly related to their critical slowing down and not related to this phenomenon. Moreover, we study Welch's PSD estimate performance for both a discrete-time Twitter segment model and real Twitter segments.…”

“…Te following is a fairly brief description of the computational methods. A detailed description of the methods is presented in the paper [28].…”

“…Terefore, a precursor signaling the self-organization of the system to the edge of a phase transition is a sharp increase in the values of the σ 2 k 􏼈 􏼉 and ρ k 􏼈 􏼉, as well as a sharp increase followed by a sharp decline in the values of the κ k 􏼈 􏼉 and c k 􏼈 􏼉. Moreover, if the system is at the edge of a phase transition, then ρ � 1 (e.g., see papers [1,28]).…”

“…Te precursor of the system self-organization to the edge of a phase transition is also an increase in the values of the series β t 􏼈 􏼉 as the system approaches τ c , which corresponds to an increase in spectral power at low frequencies. Moreover, if the system is on the edge of a phase transition, then 1 ≤ β ≤ 2 ("ficker" efect) (e.g., see the papers [28,36]). Te exponent estimate β is a statistical estimate of the power-law tangent for the PSD, S(f) � f − β , on a double logarithmic scale.…”

“…Previously (see the paper [28]), we introduced the concept of the efectiveness of EWM and investigated the efectiveness of the measures in early warning in Sandpile Cellular Automata (SCA) self-organization to the edge of a phase transition. SCA is isomorphic to Twitter with a suitable choice of local rules and topological structure of the graph (lattice).…”