Saddle-Node Bifurcation and Homoclinic Persistence in AFM with Periodic Forcing
Dynamical Systems
2019-08-19 v1
Abstract
We study the dynamics of an Atomic Force Microscope (AFM) model, under the Lennard-Jones force with non-linear damping, and harmonic forcing. We establish the bifurcation diagrams for equilibria in a conservative system. Particularly, we present conditions that guarantee the local existence of saddle-node bifurcations. By using the Melnikov method, the region in the space parameters where the persistence of homoclinic orbits is determined in a non-conservative system.
Keywords
Cite
@article{arxiv.1908.05777,
title = {Saddle-Node Bifurcation and Homoclinic Persistence in AFM with Periodic Forcing},
author = {Alexander Gutierrez G. and Daniel Cortés Z. and Diego A. and Castro G},
journal= {arXiv preprint arXiv:1908.05777},
year = {2019}
}