Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1

In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoret…