  This paper is a theoretical and a numerical investigation of the stability of
a tip-cantilever system used in Non-Contact Atomic Force Microscopy (NC-AFM)
when it oscillates close to a surface. No additional dissipative force is
considered. The theoretical approach is based on a variationnal method
exploiting a coarse grained operation that gives the temporal dependence of the
nonlinear coupled equations of motion in amplitude and phase of the oscillator.
Stability criterions for the resonance peak are deduced and predict a stable
behavior of the oscillator in the vicinity of the resonance. The numerical
approach is based on results obtained with a virtual NC-AFM developped in our
group. The effect of the size of the stable domain in phase is investigated.
These results are in particularly good agreement with the theoretical
predictions. Also they show the influence of the phase shifter in the feedback
loop and the way it can affect the damping signal.
