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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.
Abstract:
In this paper, we study the phenomena of collapse and anomalous diffusion in shared mobility systems. In particular, we focus on a fleet of vehicles moving through a stations network and analyse the effect of self-journeys in system stability, using a mathematical simplex under stochastic flows. With a birth-death process approach, we find analytical upper bounds for random walk and we monitor how the system collapses by super diffusing under different randomization conditions. Using the multi-scale entropy metric, we show that real data from a bike-sharing fleet in the city of Salamanca (Spain) present a complex behaviour with more of a 1/f signal than a disorganized system with a white noise signal.
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