A nonlinear evolutionary equation modelling a dockless bicycle-sharing system

We model the operation of a dockless bicycle-sharing system by two groups of interacting components, bicycles on a sidewalk and users of the system. The model illustrates the bicycle-sharing system by a nonlinear evolutionary equation about the density of bikes on the sidewalk. Users’ behaviours, which are some straightforward and necessary actions, determine coefficients of the nonlinear evolutionary equation. Some nontrivial solutions to the equation show that even if every user has no malice, and the environment is stable, it is still possible that heaps of shared-bicycles appear somewhere along the road. Based on the data of heaps, parameters of users’ psychological models can be obtained. A numerical simulation shows how to calculate features of users and change the supply of bicycles into the system.