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This paper introduces a method for forecasting the arrival of trains by analyzing track vibration signals. The proposed algorithms, based on H‐ranks of track vibration signals, can generate early alerts for approaching trains. These algorithms are robust to additive noise and environmental conditions. The theoretical foundation of the method involves the application of matrix operations to detect significant changes in vibration patterns, indicating an approaching train. [ABSTRACT FROM AUTHOR]

The impact of power-law memory on the dynamics of the Caputo standard fractional map is investigated in this paper. The definition of a complexity measure for the Caputo standard fractional map is introduced. This measure evaluates both the average algebraic complexity of a trajectory and the distribution of the trajectories of different types in the phase space of the system. The interplay between the small-scale spatial chaos and the large-scale spatial behavior is observed and measured during the transition of the Caputo standard fractional map from the circle map to the classical standard map. It is demonstrated that the impact of the fractional derivative on the complexity of the fractional system is not straightforward and is predetermined by the physical properties governing the dynamics of that system. [ABSTRACT FROM AUTHOR]