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A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems.

Francisco Prieto-Castrillo1, Javier Borondo2, Rubén Martín García3

  • 1Facultad de Ciencias, Departamento de Matemáticas, Universidad de Oviedo, Calle Federico García Lorca 18, 33007 Oviedo, Spain.

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|May 28, 2022
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Summary

Shared mobility systems can collapse due to self-journeys, leading to super-diffusion. Analysis of a bike-sharing fleet reveals complex, 1/f-like behavior, not random white noise, indicating system instability.

Keywords:
complexitydeath-birth processesmulti-scale entropyshared mobility systemssuper diffusion

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Area of Science:

  • Complex systems science
  • Transportation network analysis
  • Mathematical modeling

Background:

  • Shared mobility systems, like bike-sharing, are increasingly prevalent.
  • Understanding system stability and collapse dynamics is crucial for efficient operation.
  • Self-journeys (vehicles moving without passengers) can impact fleet dynamics.

Purpose of the Study:

  • To investigate the collapse phenomena and anomalous diffusion in shared mobility.
  • To analyze the effect of self-journeys on system stability using mathematical models.
  • To characterize the underlying signal of real-world shared mobility data.

Main Methods:

  • Mathematical simplex modeling under stochastic flows.
  • Birth-death process for analyzing random walk dynamics.
  • Multi-scale entropy (MSE) metric for signal complexity analysis.

Main Results:

  • Analytical upper bounds for random walk behavior were derived.
  • System collapse was observed through super-diffusion under varying randomization.
  • Real bike-sharing data exhibited complex 1/f-like scaling, not white noise.

Conclusions:

  • Self-journeys contribute to system instability and collapse in shared mobility.
  • The observed 1/f signal suggests underlying deterministic or complex dynamics, not pure randomness.
  • Mathematical and entropy analyses provide insights into shared mobility system behavior.