Stability of an AFM-based sliding system

The AFM system have been widely used in probing and imaging the surface property at atomic-resolution as well as measuring friction at the nanoscale. We present an analytic model of the AFM system that imitates the AFM tip as a 1D array of particles moving on a rigid substrate, and study its stability under a constant driving velocity. We reveal that both the center of the mass of the particle array and the single particles are ultimately bounded under certain conditions of the system parameters. We also provide sufficient conditions on the system parameters using Lyapunov stability theory based methods. Our theoretical claim is in consistent with the simulation results and provides guidance on choosing appropriate parameters to affect the system stability.