Saddle-Node Bifurcation and Homoclinic Persistence in AFMs with Periodic Forcing

Alexánder Gutiérrez Gutiérrez, Daniel Cortés Zapata and Diego Alexánder Castro Guevara

Mathematical Problems in Engineering, 2019, vol. 2019, 1-6

Abstract:

We study the dynamics of an atomic force microscope (AFM) model, under the Lennard-Jones force with nonlinear 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 homoclinic orbits persist is determined in a nonconservative system.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8925687

DOI: 10.1155/2019/8925687

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