A city's bicycle-sharing scheme links its stations by rebalancing-truck routes into…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Synchronisation, cascades and the resilience of networks

Problem

A city's bicycle-sharing scheme links its stations by rebalancing-truck routes into an Erdos-Renyi random network with mean degree ⟨k⟩=3\langle k\rangle = 3. Rebalancing schedules at each station are modelled as a phase oscillator; the all-to-all coupling that would entrain every station's schedule is K0=1.8 rad day−1K_0 = 1.8\,\mathrm{rad\,day^{-1}}. ((a)) Estimate the coupling KcK_{\rm c} at which the real route network begins to entrain the stations' schedules. Use κ1≈⟨k⟩+1\kappa_1\approx\langle k\rangle+1 for an Erdos-Renyi graph and Kc≈K0/κ1K_{\rm c}\approx K_0/\kappa_1. ((b)) Stations close at random for maintenance. Using the random-failure percolation threshold, find the fraction of stations that must close before the route network's giant component disappears.

Browse the problem library