## Abstract

In the following paper, we present a nonlinear model of an atomic force microscope considering the potential of Lennard–Jones and the nonlinear friction produced by the squeeze film damping effect, between the cantilever and the sample. Specifically, we study the existence and stability of periodic solutions using the lower and upper solution method in the system without friction. The condition for persistence of the homocline orbit was established by Melnikov method when the model has nonlinear friction. In this sense, the analytic and numerical approach is presented to verify the solutions of the model.

© 2020 Optical Society of America

Full Article | PDF Article**OSA Recommended Articles**

H. Nanjo, P. Qian, N. Sanada, T. M. Suzuki, H. Takahashi, H. Ito, and K. Komatsu

Opt. Lett. **25**(15) 1107-1109 (2000)

Fabien Amiot and Jean Paul Roger

Appl. Opt. **45**(30) 7800-7810 (2006)

Huimin Xie, Chai Gin Boay, Tong Liu, Yunguang Lu, Jin Yu, and Anand Asundi

Appl. Opt. **40**(34) 6193-6198 (2001)