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In the present work, we study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Derjaguin-Muller-Toporov forces and subject to imposed slow harmonic base displacement. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. Then, the charts of behaviors of the different operating modes of the AFM are determined. The dynamic saddle-node bifurcations of the contact and the noncontact invariant slow manifolds are found to be responsible for the occurrence of the tapping mode.

Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion