A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems
Francisco Prieto-Castrillo,
Javier Borondo,
Rubén Martín García,
Rosa M. Benito
Affiliations
Francisco Prieto-Castrillo
Facultad de Ciencias, Departamento de Matemáticas, Universidad de Oviedo, Calle Federico García Lorca 18, 33007 Oviedo, Spain
Javier Borondo
Facultad de Ciencias Económicas y Empresariales (ICADE), Departamento de Gestión Empresarial, Universidad Pontificia Comillas, Calle Alberto Aguilera 23, 28015 Madrid, Spain
Rubén Martín García
Facultad de Informática, Universidad Pontificia de Salamanca, Calle Compañía, 5, 37002 Salamanca, Spain
Rosa M. Benito
Grupo de Sistemas Complejos, E.T.S. de Ingeniería Agron., Alim. y de Biosist., Universidad Politécnica de Madrid, Avda. Puerta de Hierro 2-4, 28040 Madrid, Spain
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.
