Complex dynamics in a harmonically excited Lennard-Jones oscillator: Microcantilever-sample interaction in scanning probe microscopes

In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynam ical behavior of a harmonically forced system. Using nonlinear analysis tec hniques on attracting limit sets, we numerically verify the presence of cha otic invariant sets. The chaotic behavior appears to be generated via a cas cade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained fo r values of parameters predicted by Melnikov theory. Moreover, the numerica l analysis can be fruitfully employed to analyze the region of the paramete r space where no theoretical information on the presence of a chaotic invar iant set is available. In addition to explaining the experimentally observe d chaotic behavior, this analysis can be useful in finding a controller tha t stabilizes the system on a nonchaotic trajectory. The analysis can also b e used to change the AFM operating conditions to a region of the parameter space where regular motion is ensured. [S0022-0434(00)01401-5].