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.
Keywords: complexity; death-birth processes; multi-scale entropy; shared mobility systems; super diffusion.