Abstract: The dynamic behaviors of homoclinic orbits，multi-period oscillation and quasi-period oscillation of

an atomic chain are investigated by the one-dimensional Frenkel-Kontorova model. Firstly，the hyperbolic saddle

focus existed in the system is decided by the eigenvalues of Jacobian matrix. Secondly，the condition of system generation

homoclinic orbits is determined via Silnikov theorem at the hyperbolic saddle focus. Finally，the numerical

simulation is used to verify the existence of homoclinic orbits，multi-period oscillation and quasi-period oscillation

of the system. The results of this paper also provide a valuable reference for the study of solid friction phenomena.

Key words: one-dimensional Frenkel-Kontorova model, homoclinic orbits, multi-period oscillation, quasiperiod oscillation, hyperbolic saddle focus