Phase-plane dynamics of an atomic force microscope cantilever.

[danber]

Hello,

A sinusoidally driven and undisturbed cantilever of an atomic force microscope (AFM) oscillates ideally in a sinusoidal fashion but the motion of the cantilever (time-domain trajectory) can become more complicated when it is disturbed by the inter-atomic forces as the cantilever taps on the sample surface. The cantilever dynamics can be better understood in the phase-plane. An undisturbed cantilever shows elliptical trajectories in the phase-plane around a center. On the other hand, a disturbed cantilever can show nonlinear effects like period-doubling, bifurcation and chaos.

I'd like to know what can be said about the phase-plane trajectory in terms of the attractor, basin of attraction or the possibility of chaos as shown in the attachement containing my experimental data? In the beginning the phase-plane trajectories circle around a center and as the signal size increases, these trajectories also grow in size and the center transforms into a set of two centers.

Thanks.

 

[Andy Resnick]

Google is your friend:

http://iopscience.iop.org/0957-4484/17/7/S19
http://prl.aps.org/abstract/PRL/v96/i3/e036107
http://link.springer.com/article/10.1007/s11071-005-9009-5#page-1
http://chaosbook.org/projects/Kasivajhula/afmchaos.pdf
http://pic.sagepub.com/content/early/2012/11/21/0954406212467933.full.pdf

 

[danber]

Thanks.

I already know the papers by Raman and Jamitzky but they've done experiments aimed at observing chaos in AFM and I've a different experiment where I'm not forcing the cantilever motion to be chaotic but observing breakdown of the cantilever trajectory in time-domain and the phase-plane trajectory shows a specific attractor which doesn't seem to be a chaotic one but still is markedly different from that of a harmonic oscillator.

I think time series analysis of the given experimental data can be helpful but my question was how to understand the attractor from a purly dynamical point of view?