Stability of coupled oscillators using Frenkel-Kontorova model

We study the stability of coupled oscillators motivated by the Frenkel-Kontorova (FK) model. The FK model describes a chain of classical particles coupled to their neighbors and subject to a periodic on-site potential. The open-loop system of the FK model represents interconnected oscillators that have locally stable or unstable equilibrium points. We reveal the stability of the coupled system in the presence of linear and nonlinear particle interactions, respectively, and verify the results by numerical simulations. The result applies to physical systems such as atomic-scale friction whose dynamics is described by the FK model.